Solve 2(x-6)geq3(1-x)

$$2 ( x - 6 ) \geq 3 ( 1 - x )$$

Solve for x

$$x\geq 3$$

Solution Steps

Use the distributive property to multiply 2 by x-6.

$$2x-12\geq 3\left(1-x\right)$$

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

$$2x-12\geq 3-3x$$

Add 3x to both sides.

$$2x-12+3x\geq 3$$

Combine 2x and 3x to get 5x.

$$5x-12\geq 3$$

Add 12 to both sides.

$$5x\geq 3+12$$

Add 3 and 12 to get 15.

$$5x\geq 15$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\geq \frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x\geq 3$$