Solve x+3(2x-1)geqx

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

Solve for x

$$x\geq \frac{1}{2}$$

Solution Steps

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

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

Combine x and 6x to get 7x.

$$7x-3\geq x$$

Subtract x from both sides.

$$7x-3-x\geq 0$$

Combine 7x and -x to get 6x.

$$6x-3\geq 0$$

Add 3 to both sides. Anything plus zero gives itself.

$$6x\geq 3$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x\geq \frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$x\geq \frac{1}{2}$$