Solve 4(x-6)+3x-5geq3(x-7)+12x

$$4 ( x - 6 ) + 3 x - 5 \geq 3 ( x - 7 ) + 12 x$$

Solve for x

$$x\leq -1$$

Solution Steps

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

$$4x-24+3x-5\geq 3\left(x-7\right)+12x$$

Combine 4x and 3x to get 7x.

$$7x-24-5\geq 3\left(x-7\right)+12x$$

Subtract 5 from -24 to get -29.

$$7x-29\geq 3\left(x-7\right)+12x$$

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

$$7x-29\geq 3x-21+12x$$

Combine 3x and 12x to get 15x.

$$7x-29\geq 15x-21$$

Subtract 15x from both sides.

$$7x-29-15x\geq -21$$

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

$$-8x-29\geq -21$$

Add 29 to both sides.

$$-8x\geq -21+29$$

Add -21 and 29 to get 8.

$$-8x\geq 8$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x\leq \frac{8}{-8}$$

Divide 8 by -8 to get -1.

$$x\leq -1$$