Bot GPT 4-o mini 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 \(-1\).
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