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

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.

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 = 

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

Tbis is the given inequality.

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 = 

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

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.

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.

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.

The area of the right-angled triangle =
=
Inequality representing the area of triangle =

8 < 2(x + 4)
- 8 < 2x + 8
- 16 < 2x
- 8 < x
- 3x + 4 > x - 4
- 3x + 8 > x
8 > 4x
2 > x
So, - 8 < x < 2

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

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

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.

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

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

The compound inequality 12 < 2x < 28 involves “and.”
Solving 12 < 2x

6 < x
x > 6
Solving 2x < 28

x < 14
So, the solution of the inequality given is “x > 6 and x < 14” or “6 < x < 14.”