Maths-
General
Easy

Question

Which of the following Compound inequalities have the solution x < 3, select all that apply.

  1. 3x+5 < 6 or -2x+9 > 3
  2. 3x+5 < 6 and -2x+9 > 3
  3. 3x-5 < 10 and -2x+9 > 3
  4. 3x-5 < 10 or -2x+9 < 3

hintHint:

If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
 

The correct answers are: 3x+5 < 6 or -2x+9 > 3, 3x-5 < 10 and -2x+9 > 3, 3x-5 < 10 or -2x+9 < 3


    Solving, 3x+5 < 6

    3x < 1

    x less than 1 third
    Solving, -2x+9 > 3

    -2x > -6

    x < 3
    Solving, 3x-5 < 10

    3x < 15

    x < 5
    Solving, -2x+9 < 3

    -2x < -6

    x > 3
    Solution for 3x+5 < 6 or -2x+9 > 3 or we can say x <  or  x < 3 is x < 3
    Graph for 3x+5 < 6 and -2x+9 > 3 or we can say x <  and x < 3 is x < .
    Graph for 3x-5 < 10 and -2x+9 > 3 or we can say x < 5 and x < 3 is x < 3
    Graph for  3x-5 < 10 or -2x+9 < 3 or we can say x < 5 or x > 3 is all real numbers
    Final Answer:
    Hence, options A, C and D are correct as all these solutions include x < 3.

    You can also follow these steps to solve the compound inequality with the equation for example: 3x + 5 < 6:
    Subtract 5 from both sides.
    3x + 5 - 5 < 6 - 5
    Simplify and subtract the numbers.
    And we get, 3 x < 1
    Divide both sides by the same factor.
    3x/3 < 1/3
    Cancel terms that are in both the numerator and denominator.
    and the solution is x < 1/3.

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