Solve 3(x-5)geq7-4(3-2x)

$$3 ( x - 5 ) \geq 7 - 4 ( 3 - 2 x )$$

Solve for x

$$x\leq -2$$

Solution Steps

Use the distributive property to multiply 3 by x-5.

$$3x-15\geq 7-4\left(3-2x\right)$$

Use the distributive property to multiply -4 by 3-2x.

$$3x-15\geq 7-12+8x$$

Subtract 12 from 7 to get -5.

$$3x-15\geq -5+8x$$

Subtract 8x from both sides.

$$3x-15-8x\geq -5$$

Combine 3x and -8x to get -5x.

$$-5x-15\geq -5$$

Add 15 to both sides.

$$-5x\geq -5+15$$

Add -5 and 15 to get 10.

$$-5x\geq 10$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\leq \frac{10}{-5}$$

Divide 10 by -5 to get -2.

$$x\leq -2$$