Solve 17(2+2x)geq4(-x-10)

$$17 ( 2 + 2 x ) \geq 4 ( - x - 10 )$$

Solve for x

$$x\geq -\frac{37}{19}$$

Solution Steps

Use the distributive property to multiply 17 by 2+2x.

$$34+34x\geq 4\left(-x-10\right)$$

Use the distributive property to multiply 4 by -x-10.

$$34+34x\geq 4\left(-x\right)-40$$

Subtract 4\left(-x\right) from both sides.

$$34+34x-4\left(-x\right)\geq -40$$

Multiply -1 and 4 to get -4.

$$34+34x-4\left(-1\right)x\geq -40$$

Multiply -4 and -1 to get 4.

$$34+34x+4x\geq -40$$

Combine 34x and 4x to get 38x.

$$34+38x\geq -40$$

Subtract 34 from both sides.

$$38x\geq -40-34$$

Subtract 34 from -40 to get -74.

$$38x\geq -74$$

Divide both sides by 38. Since 38 is positive, the inequality direction remains the same.

$$x\geq \frac{-74}{38}$$

Reduce the fraction \frac{-74}{38} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{37}{19}$$