Solve 2(x-2)leq4(x+6)

$$2 ( x - 2 ) \leq 4 ( x + 6 )$$

Solve for x

$$x\geq -14$$

Solution Steps

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

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

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

$$2x-4\leq 4x+24$$

Subtract 4x from both sides.

$$2x-4-4x\leq 24$$

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

$$-2x-4\leq 24$$

Add 4 to both sides.

$$-2x\leq 24+4$$

Add 24 and 4 to get 28.

$$-2x\leq 28$$

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

$$x\geq \frac{28}{-2}$$

Divide 28 by -2 to get -14.

$$x\geq -14$$