Solve 2(x-3)+1leq3(2x+6)-3

$$2 ( x - 3 ) + 1 \leq 3 ( 2 x + 6 ) - 3$$

Solve for x

$$x\geq -5$$

Solution Steps

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

$$2x-6+1\leq 3\left(2x+6\right)-3$$

Add -6 and 1 to get -5.

$$2x-5\leq 3\left(2x+6\right)-3$$

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

$$2x-5\leq 6x+18-3$$

Subtract 3 from 18 to get 15.

$$2x-5\leq 6x+15$$

Subtract 6x from both sides.

$$2x-5-6x\leq 15$$

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

$$-4x-5\leq 15$$

Add 5 to both sides.

$$-4x\leq 15+5$$

Add 15 and 5 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.

$$x\geq -5$$