Solve 2(x-3)+4leq3(2x+6)

$$2 ( x - 3 ) + 4 \leq 3 ( 2 x + 6 )$$

Solve for x

$$x\geq -5$$

Solution Steps

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

$$2x-6+4\leq 3\left(2x+6\right)$$

Add -6 and 4 to get -2.

$$2x-2\leq 3\left(2x+6\right)$$

Use the distributive property to multiply 3 by 2x+6.

$$2x-2\leq 6x+18$$

Subtract 6x from both sides.

$$2x-2-6x\leq 18$$

Combine 2x and -6x to get -4x.

$$-4x-2\leq 18$$

Add 2 to both sides.

$$-4x\leq 18+2$$

Add 18 and 2 to get 20.

$$-4x\leq 20$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\geq \frac{20}{-4}$$

Divide 20 by -4 to get -5.

$$x\geq -5$$