Solve 3(x+2)-1geq1-2(x-1)

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

Solve for x

$$x\geq -\frac{2}{5}$$

Solution Steps

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

$$3x+6-1\geq 1-2\left(x-1\right)$$

Subtract 1 from 6 to get 5.

$$3x+5\geq 1-2\left(x-1\right)$$

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

$$3x+5\geq 1-2x+2$$

Add 1 and 2 to get 3.

$$3x+5\geq 3-2x$$

Add 2x to both sides.

$$3x+5+2x\geq 3$$

Combine 3x and 2x to get 5x.

$$5x+5\geq 3$$

Subtract 5 from both sides.

$$5x\geq 3-5$$

Subtract 5 from 3 to get -2.

$$5x\geq -2$$

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

$$x\geq -\frac{2}{5}$$