Solve 5(x+2)geq1-2(x-1)

$$5 ( x + 2 ) \geq 1 - 2 ( x - 1 )$$

Solve for x

$$x\geq -1$$

Solution Steps

Use the distributive property to multiply 5 by x+2.

$$5x+10\geq 1-2\left(x-1\right)$$

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

$$5x+10\geq 1-2x+2$$

Add 1 and 2 to get 3.

$$5x+10\geq 3-2x$$

Add 2x to both sides.

$$5x+10+2x\geq 3$$

Combine 5x and 2x to get 7x.

$$7x+10\geq 3$$

Subtract 10 from both sides.

$$7x\geq 3-10$$

Subtract 10 from 3 to get -7.

$$7x\geq -7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\geq \frac{-7}{7}$$

Divide -7 by 7 to get -1.

$$x\geq -1$$