Solve 4(x+5)+8geq5(x+2)

$$4 ( x + 5 ) + 8 \geq 5 ( x + 2 )$$

Solve for x

$$x\leq 18$$

Solution Steps

Use the distributive property to multiply 4 by x+5.

$$4x+20+8\geq 5\left(x+2\right)$$

Add 20 and 8 to get 28.

$$4x+28\geq 5\left(x+2\right)$$

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

$$4x+28\geq 5x+10$$

Subtract 5x from both sides.

$$4x+28-5x\geq 10$$

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

$$-x+28\geq 10$$

Subtract 28 from both sides.

$$-x\geq 10-28$$

Subtract 28 from 10 to get -18.

$$-x\geq -18$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq \frac{-18}{-1}$$

Fraction \frac{-18}{-1} can be simplified to 18 by removing the negative sign from both the numerator and the denominator.

$$x\leq 18$$