Mathematics
Grade10
Easy

Question

A compound inequality including “or” has the solutions of ___________.

  1. Only the first inequality statement
  2. Only the second inequality statement
  3. Either of the inequalities
  4. Both the inequalities

Hint:

This is a question of compound inequalities. A compound inequality means we are given two statements. It is joined using the words “and” and “or”. We have to find the values of the variables satisfying those statements.

The correct answer is: Either of the inequalities


    We are asked about the word “or”.
    When the word “and” is used, the values of the variables simultaneously satisfy both the inequalities.
    If we plot the solutions on a graph, the final graph will be intersection of both the inequalities.
    When the word “or” is used, the values of the variables satisfy either of the inequalities.
    If we plot the solution graph, the final graph will show solutions of either of inequalities.
    So, a compound inequality including “or” has the solutions of either of the inequalities.

    Whenever we solve questions of inequality, we have to check for the words “and” and “or”.

    Related Questions to study

    Grade10
    Mathematics

    Solve 32 < 2x < 46.

    The given statement is 32 < 2x < 46.
    The quantity 2x is less than 46 and is greater than 32.
    We will solve the problem using the rules to solve the inequalities.
    We have to perform the same operation on all three terms.
    32 < 2x < 46
    We will divide all the three terms by 2. The sign of inequality is not flipped as we are dividing by positive numbers.
    16 < x < 23
    We cannot simplify it further.
    So, the final answer is 16 < x < 23.

    Solve 32 < 2x < 46.

    MathematicsGrade10
    The given statement is 32 < 2x < 46.
    The quantity 2x is less than 46 and is greater than 32.
    We will solve the problem using the rules to solve the inequalities.
    We have to perform the same operation on all three terms.
    32 < 2x < 46
    We will divide all the three terms by 2. The sign of inequality is not flipped as we are dividing by positive numbers.
    16 < x < 23
    We cannot simplify it further.
    So, the final answer is 16 < x < 23.
    Grade10
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    Find the area of the right-angled triangle if the height is 11 units and the base is x units, given that the area of the triangle lies between 17 and 42 sq. units

    The height of the right-angled triangle is 11 units.
    The base of the right-angled triangle is x units.
    The area lies between the 17sq. units and 42sq. units. So, this question is of inequality. We have to write the mathematical form of this inequality.
    The area of a right-angled triangle is given as follows:
    Area = 1 half cross times 11 cross times x
    equals fraction numerator 11 x over denominator 2 end fraction
    Now, we will see the limits.
    The area lies between 17sq. units and 42sq. units.
    It means the area should be greater than 17sq. units and less than 42sq. units.
    So, we can write
    17 < Area < 42
    17 less than fraction numerator 11 x over denominator 2 end fraction less than 42
    Tbis is the given inequality.

    Find the area of the right-angled triangle if the height is 11 units and the base is x units, given that the area of the triangle lies between 17 and 42 sq. units

    MathematicsGrade10
    The height of the right-angled triangle is 11 units.
    The base of the right-angled triangle is x units.
    The area lies between the 17sq. units and 42sq. units. So, this question is of inequality. We have to write the mathematical form of this inequality.
    The area of a right-angled triangle is given as follows:
    Area = 1 half cross times 11 cross times x
    equals fraction numerator 11 x over denominator 2 end fraction
    Now, we will see the limits.
    The area lies between 17sq. units and 42sq. units.
    It means the area should be greater than 17sq. units and less than 42sq. units.
    So, we can write
    17 < Area < 42
    17 less than fraction numerator 11 x over denominator 2 end fraction less than 42
    Tbis is the given inequality.
    Grade10
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    The inequality that is represented by graph 2 is ______.

    STEP BY STEP SOLUTION
    In the graph 2 x is geater than or equals to -2 but less that 5
    So, The inequality that is represented by graph 2 is - 2 ≤ x < 5.
    Inequality = negative 2 less or equal than space x space less than 5

    The inequality that is represented by graph 2 is ______.

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    STEP BY STEP SOLUTION
    In the graph 2 x is geater than or equals to -2 but less that 5
    So, The inequality that is represented by graph 2 is - 2 ≤ x < 5.
    Inequality = negative 2 less or equal than space x space less than 5
    parallel
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    The solution of 2 < x ≤ 8 is ________.

    Given: 2 < x ≤ 8
    So, the numbers can be 3, 4, 5, 6, 7, 8.
    Thus, the solution of 2 < x ≤ 8 is 3, 4, 5, 6, 7, 8.
    Hence, option(b) is the correct option.

    The solution of 2 < x ≤ 8 is ________.

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    Given: 2 < x ≤ 8
    So, the numbers can be 3, 4, 5, 6, 7, 8.
    Thus, the solution of 2 < x ≤ 8 is 3, 4, 5, 6, 7, 8.
    Hence, option(b) is the correct option.
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    Write the inequality represented by the graph

    The graph shown in the figure represents inequality x ≤ -1.2 and x ≥ - 0.4
    Hence, option(c) is the correct option.

    Write the inequality represented by the graph

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    The graph shown in the figure represents inequality x ≤ -1.2 and x ≥ - 0.4
    Hence, option(c) is the correct option.
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    Write an inequality to represent the following:
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    We have to write an expression for a number greater than 5.
    Let the number be x. Then,
    x > 5.
    Hence, the correct option is B.

    Write an inequality to represent the following:
    Any number greater than 5

    MathematicsGrade10
    We have to write an expression for a number greater than 5.
    Let the number be x. Then,
    x > 5.
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    What is the solution of 0.2 x -4 - 2x < - 0.4 and 3x + 2.7 <3 ?

    The given inequalities are as follows:
    0.2x – 4 – 2x < -0.4 and 3x + 2.7 < 3
    The word used to join them is “and”. So, we have to find the values of x satisfying both the statements.
    When the word “and” is used, the values of the variables simultaneously satisfy both the inequalities.
    When the word “or” is used, the values of the variables satisfy either of the inequalities.
    We will solve the inequalities one by one.
    0.2x – 4 – 2x < -0.4
    We will take the variables together and solve them first.
    0.2x – 2x – 4 < - 0.4
    - 1.8x – 4 < - 0.4
    We will isolate the variable by adding 4 to both the sides.
    -1.8x – 4 + 4 < -0.4 + 4
    - 1.8x < 3.6
    Now, we will divide both the sides by -1.8. As we are dividing by a negative number, the inequality will flip.
    fraction numerator negative 1.8 x over denominator negative 1.8 end fraction greater than fraction numerator 3.6 over denominator negative 1.8 end fraction
    x  >  -2
    3x + 2.7 < 3
    We will isolate the variable by subtracting 2.7 from both the sides.
    3x + 2.7 – 2.7 < 3 – 2.7
    3x < 0.3
    Dividing both the sides by 3 we get,
    x < 0.1
    Now, the values satisfying the two inequalities are given as follows:
    x > -2
    x < 0.1
    We can combine the solution and write the intersection of the solution as follow:
    -2 < x < 0.1
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    What is the solution of 0.2 x -4 - 2x < - 0.4 and 3x + 2.7 <3 ?

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    The given inequalities are as follows:
    0.2x – 4 – 2x < -0.4 and 3x + 2.7 < 3
    The word used to join them is “and”. So, we have to find the values of x satisfying both the statements.
    When the word “and” is used, the values of the variables simultaneously satisfy both the inequalities.
    When the word “or” is used, the values of the variables satisfy either of the inequalities.
    We will solve the inequalities one by one.
    0.2x – 4 – 2x < -0.4
    We will take the variables together and solve them first.
    0.2x – 2x – 4 < - 0.4
    - 1.8x – 4 < - 0.4
    We will isolate the variable by adding 4 to both the sides.
    -1.8x – 4 + 4 < -0.4 + 4
    - 1.8x < 3.6
    Now, we will divide both the sides by -1.8. As we are dividing by a negative number, the inequality will flip.
    fraction numerator negative 1.8 x over denominator negative 1.8 end fraction greater than fraction numerator 3.6 over denominator negative 1.8 end fraction
    x  >  -2
    3x + 2.7 < 3
    We will isolate the variable by subtracting 2.7 from both the sides.
    3x + 2.7 – 2.7 < 3 – 2.7
    3x < 0.3
    Dividing both the sides by 3 we get,
    x < 0.1
    Now, the values satisfying the two inequalities are given as follows:
    x > -2
    x < 0.1
    We can combine the solution and write the intersection of the solution as follow:
    -2 < x < 0.1
    So, the solution is -2 < x < 0.1.
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    Find the area of the right-angled triangle if the height is 5 units and the base is x units, given that the area of the triangle lies between 10 and 35 sq. units

    The area of the right-angled triangle =1 half space cross times space 5 space cross times space x
    =fraction numerator 5 x over denominator 2 end fraction
    Inequality representing the area of triangle = 10 less than fraction numerator 5 x over denominator 2 end fraction less than 35

    Find the area of the right-angled triangle if the height is 5 units and the base is x units, given that the area of the triangle lies between 10 and 35 sq. units

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    The area of the right-angled triangle =1 half space cross times space 5 space cross times space x
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    Solve - 8 < 2  (x + 4) or - 3x + 4 > x - 4

    8 < 2(x + 4)
    - 8 < 2x + 8
    - 16 < 2x
    - 8 < x
    - 3x + 4 > x - 4
    - 3x + 8 > x
    8 > 4x
    2 > x
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    Solve - 8 < 2  (x + 4) or - 3x + 4 > x - 4

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    8 < 2(x + 4)
    - 8 < 2x + 8
    - 16 < 2x
    - 8 < x
    - 3x + 4 > x - 4
    - 3x + 8 > x
    8 > 4x
    2 > x
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    parallel
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    Write the compound inequality that represents the area A of the rectangle if 35 ≥ A ≥ 25.

    Step by step solution:
    The compound function representing the area of the rectangle is  35 ≥ A ≥ 25 [given]
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    rightwards double arrow35 ≥ 5x ≥ 25      [ A = 5x]
    Hence, option(d) is the correct option.

    Write the compound inequality that represents the area A of the rectangle if 35 ≥ A ≥ 25.

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    Step by step solution:
    The compound function representing the area of the rectangle is  35 ≥ A ≥ 25 [given]
    Now, 35 ≥ A ≥ 25
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    Hence, option(d) is the correct option.
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    The inequality that is represented by graph 4 is ______.

    The inequality that is represented by graph 4 is - 2 ≤ x ≤ 5.
    Hence, option(d) is the correct option.

    The inequality that is represented by graph 4 is ______.

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    The inequality that is represented by graph 4 is - 2 ≤ x ≤ 5.
    Hence, option(d) is the correct option.
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    Mathematics

    The compound function that represents the graph is __________.

    The inequality represented by the graph talks about the numbers less than or equal to -4 and greater than or equal to -1.
    The inequalities will be x ≤ - 4 and x ≥ - 1
    Hence, option(b) is the correct option.

    The compound function that represents the graph is __________.

    MathematicsGrade10
    The inequality represented by the graph talks about the numbers less than or equal to -4 and greater than or equal to -1.
    The inequalities will be x ≤ - 4 and x ≥ - 1
    Hence, option(b) is the correct option.
    parallel
    Grade10
    Mathematics

    Write a compound inequality for the given graph

    step by step solution:
    The compound inequality that represents the given data is - 5 ≤ x ≤ - 1.
    Hence, option(d) is the correct option.

    Write a compound inequality for the given graph

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    step by step solution:
    The compound inequality that represents the given data is - 5 ≤ x ≤ - 1.
    Hence, option(d) is the correct option.
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    Which inequality is the same as “pick a number between -3 and 7?”

    The inequality that represents the statement “pick a number between - 3 and 7” is  - 3 < x < 7.
    Hence, option(d) is the correct option.

    Which inequality is the same as “pick a number between -3 and 7?”

    MathematicsGrade10
    The inequality that represents the statement “pick a number between - 3 and 7” is  - 3 < x < 7.
    Hence, option(d) is the correct option.
    Grade10
    Mathematics

    Solve 12 < 2x < 28

    The compound inequality 12 < 2x < 28 involves “and.”
    Solving 12 < 2x
    12 over 2 less than fraction numerator 2 x over denominator 2 end fraction
    6 < x
    x > 6
    Solving 2x < 28
    fraction numerator 2 x over denominator 2 end fraction less than 28 over 2
    x < 14
    So, the solution of the inequality given is “x > 6 and x < 14” or “6 < x < 14.”

    Solve 12 < 2x < 28

    MathematicsGrade10
    The compound inequality 12 < 2x < 28 involves “and.”
    Solving 12 < 2x
    12 over 2 less than fraction numerator 2 x over denominator 2 end fraction
    6 < x
    x > 6
    Solving 2x < 28
    fraction numerator 2 x over denominator 2 end fraction less than 28 over 2
    x < 14
    So, the solution of the inequality given is “x > 6 and x < 14” or “6 < x < 14.”
    parallel

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