Solve -9x+x-(-3+2)-(-x)>-7+8(x)

$$-9x+x-(-3+2)-(-x) > -7+8(x)$$

Solve for x

$$x<\frac{8}{15}$$

Solution Steps

Combine -9x and x to get -8x.

$$-8x-\left(-3+2\right)-\left(-x\right)>-7+8x$$

Add -3 and 2 to get -1.

$$-8x-\left(-1\right)-\left(-x\right)>-7+8x$$

The opposite of -1 is 1.

$$-8x+1-\left(-x\right)>-7+8x$$

Subtract 8x from both sides.

$$-8x+1-\left(-x\right)-8x>-7$$

Multiply -1 and -1 to get 1.

$$-8x+1+x-8x>-7$$

Combine -8x and x to get -7x.

$$-7x+1-8x>-7$$

Combine -7x and -8x to get -15x.

$$-15x+1>-7$$

Subtract 1 from both sides.

$$-15x>-7-1$$

Subtract 1 from -7 to get -8.

$$-15x>-8$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x<\frac{-8}{-15}$$

Fraction \frac{-8}{-15} can be simplified to \frac{8}{15} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{8}{15}$$