Solve 3x-8(1-x)-(x-2)geq0

$$3 x - 8 ( 1 - x ) - ( x - 2 ) \geq 0$$

Solve for x

$$x\geq \frac{3}{5}$$

Solution Steps

Use the distributive property to multiply -8 by 1-x.

$$3x-8+8x-\left(x-2\right)\geq 0$$

Combine 3x and 8x to get 11x.

$$11x-8-\left(x-2\right)\geq 0$$

To find the opposite of x-2, find the opposite of each term.

$$11x-8-x-\left(-2\right)\geq 0$$

The opposite of -2 is 2.

$$11x-8-x+2\geq 0$$

Combine 11x and -x to get 10x.

$$10x-8+2\geq 0$$

Add -8 and 2 to get -6.

$$10x-6\geq 0$$

Add 6 to both sides. Anything plus zero gives itself.

$$10x\geq 6$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x\geq \frac{6}{10}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{3}{5}$$