Question

Select all of the possible values of x:

−8x+2x−16<−5x+7x


-4


-2


0


-3


-1

Answer 1

To solve the inequality \(-8x + 2x - 16 < -5x + 7x\), we first simplify both sides.

Starting with the left side:
\[
-8x + 2x - 16 = -6x - 16
\]

Now simplifying the right side:
\[
-5x + 7x = 2x
\]

Thus, the inequality becomes:
\[
-6x - 16 < 2x
\]

Next, we add \(6x\) to both sides to isolate \(x\):
\[
-16 < 8x
\]

Now, divide both sides by \(8\):
\[
-2 < x
\]

This can also be written as:
\[
x > -2
\]

Now, we evaluate the possible values of \(x\):
- \( -4 \): Not greater than -2.
- \( -2 \): Not greater than -2.
- \( 0 \): Greater than -2.
- \( -3 \): Not greater than -2.
- \( -1 \): Greater than -2.

The possible values for \(x\) that satisfy the inequality \(x > -2\) are:
- **0**
- **-1**

Thus, the selected possible values of \(x\) are \(0\) and \(-1\).