Solve 3(2x+2)geq4(x-1)+7

$$3 ( 2 x + 2 ) \geq 4 ( x - 1 ) + 7$$

Solve for x

$$x\geq -\frac{3}{2}$$

Solution Steps

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

$$6x+6\geq 4\left(x-1\right)+7$$

Use the distributive property to multiply 4 by x-1.

$$6x+6\geq 4x-4+7$$

Add -4 and 7 to get 3.

$$6x+6\geq 4x+3$$

Subtract 4x from both sides.

$$6x+6-4x\geq 3$$

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

$$2x+6\geq 3$$

Subtract 6 from both sides.

$$2x\geq 3-6$$

Subtract 6 from 3 to get -3.

$$2x\geq -3$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\geq -\frac{3}{2}$$