Solve 6(4-3x)-5(x-3)geq3(7-x)-4(x-5)+46

$$6(4-3x)-5(x-3) \geq 3(7-x)-4(x-5)+46$$

Solve for x

$$x\leq -3$$

Solution Steps

Use the distributive property to multiply 6 by 4-3x.

$$24-18x-5\left(x-3\right)\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

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

$$24-18x-5x+15\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Combine -18x and -5x to get -23x.

$$24-23x+15\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Add 24 and 15 to get 39.

$$39-23x\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Use the distributive property to multiply 3 by 7-x.

$$39-23x\geq 21-3x-4\left(x-5\right)+46$$

Use the distributive property to multiply -4 by x-5.

$$39-23x\geq 21-3x-4x+20+46$$

Combine -3x and -4x to get -7x.

$$39-23x\geq 21-7x+20+46$$

Add 21 and 20 to get 41.

$$39-23x\geq 41-7x+46$$

Add 41 and 46 to get 87.

$$39-23x\geq 87-7x$$

Add 7x to both sides.

$$39-23x+7x\geq 87$$

Combine -23x and 7x to get -16x.

$$39-16x\geq 87$$

Subtract 39 from both sides.

$$-16x\geq 87-39$$

Subtract 39 from 87 to get 48.

$$-16x\geq 48$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\leq \frac{48}{-16}$$

Divide 48 by -16 to get -3.

$$x\leq -3$$