Solve -1(8-3x)geq9(2x-5)+7

$$- 1 ( 8 - 3 x ) \geq 9 ( 2 x - 5 ) + 7$$

Solve for x

$$x\leq 2$$

Solution Steps

To find the opposite of 8-3x, find the opposite of each term.

$$-8-\left(-3x\right)\geq 9\left(2x-5\right)+7$$

The opposite of -3x is 3x.

$$-8+3x\geq 9\left(2x-5\right)+7$$

Use the distributive property to multiply 9 by 2x-5.

$$-8+3x\geq 18x-45+7$$

Add -45 and 7 to get -38.

$$-8+3x\geq 18x-38$$

Subtract 18x from both sides.

$$-8+3x-18x\geq -38$$

Combine 3x and -18x to get -15x.

$$-8-15x\geq -38$$

Add 8 to both sides.

$$-15x\geq -38+8$$

Add -38 and 8 to get -30.

$$-15x\geq -30$$

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

$$x\leq \frac{-30}{-15}$$

Divide -30 by -15 to get 2.

$$x\leq 2$$