Question

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?

Answer 1

The values of
`\( x \)` satisfying the compound inequality
`\(-22 > -5x - 7 \geq -3\)` are
`\( x \in \left( -\infty, -(4)/(5) \right]\)` , indicating
`\( x \)` is less than or equal to
`\(-(4)/(5)\).`

To find the values of
`\( x \)` that satisfy the compound inequality
`\(-22 > -5x - 7 \geq -3\),`you can follow these steps:

1. Isolate the variable
`\( x \):`

`\[ -22 > -5x - 7 \geq -3 \]`

Add 7 to all parts of the compound inequality:

`\[ -15 > -5x \geq 4 \]`

Divide all parts by -5. Since you are dividing by a negative number, the direction of the inequality signs will change:

`\[ 3 < x \leq -(4)/(5) \]`

2. Write the solution in interval notation:

`\[ x \in \left( -\infty, -(4)/(5) \right] \]`

This indicates that \( x \) can take any value less than or equal to
`\(-(4)/(5)\).`

So, the answer is
`\( x \in \left( -\infty, -(4)/(5) \right] \).`

The probable question maybe:

What values of x satisfy the compound inequality −22 > −5x − 7 ≥ −3?