Solve 30-5(x+15)geq2(2x+7)

$$30 - 5 ( x + 15 ) \geq 2 ( 2 x + 7 )$$

Solve for x

$$x\leq -\frac{59}{9}$$

Solution Steps

Use the distributive property to multiply -5 by x+15.

$$30-5x-75\geq 2\left(2x+7\right)$$

Subtract 75 from 30 to get -45.

$$-45-5x\geq 2\left(2x+7\right)$$

Use the distributive property to multiply 2 by 2x+7.

$$-45-5x\geq 4x+14$$

Subtract 4x from both sides.

$$-45-5x-4x\geq 14$$

Combine -5x and -4x to get -9x.

$$-45-9x\geq 14$$

Add 45 to both sides.

$$-9x\geq 14+45$$

Add 14 and 45 to get 59.

$$-9x\geq 59$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x\leq -\frac{59}{9}$$