Solve 2(x-3)geq4(x+4)-10

$$2 ( x - 3 ) \geq 4 ( x + 4 ) - 10$$

Solve for x

$$x\leq -6$$

Solution Steps

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

$$2x-6\geq 4\left(x+4\right)-10$$

Use the distributive property to multiply 4 by x+4.

$$2x-6\geq 4x+16-10$$

Subtract 10 from 16 to get 6.

$$2x-6\geq 4x+6$$

Subtract 4x from both sides.

$$2x-6-4x\geq 6$$

Combine 2x and -4x to get -2x.

$$-2x-6\geq 6$$

Add 6 to both sides.

$$-2x\geq 6+6$$

Add 6 and 6 to get 12.

$$-2x\geq 12$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\leq \frac{12}{-2}$$

Divide 12 by -2 to get -6.

$$x\leq -6$$