Solve 3(2x-1)-4(x-2)geq8

$$3 ( 2 x - 1 ) - 4 ( x - 2 ) \geq 8$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-4\left(x-2\right)\geq 8$$

Use the distributive property to multiply -4 by x-2.

$$6x-3-4x+8\geq 8$$

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

$$2x-3+8\geq 8$$

Add -3 and 8 to get 5.

$$2x+5\geq 8$$

Subtract 5 from both sides.

$$2x\geq 8-5$$

Subtract 5 from 8 to get 3.

$$2x\geq 3$$

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

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