What number must be equal to A for the product 4 × a to be greater than 20 but less than 24?

Let us write down and solve this inequality.

20> 4 * a <24.

To determine the limits of the values ​​of the variable a, it is necessary to simplify this inequality. Let’s get rid of the numerical value of the variable a of the number 4, divide all the components of the inequality into it.

20/4> 4 * a / 4 <24/4.

5> a <6.

Therefore, we got that the variable a lies between the numbers 5 and 6.

For verification, consider the boundary values.

Substitute the value 5.1 instead of the variable a:

20> 4 * 5.1 <24.

20> 20.4 <24.

The inequality is fulfilled.

And also for verification, substitute the value 5.9 instead of the variable a:

20> 4 * 5.9 <24.

20> 23.6 <24.

This inequality also holds, therefore, the decision that the variable a is between the numbers 5 and 6 is correct.

Answer: 5> a <6 – number a must be greater than 5, but less than 6.