Solve 4(x+2)leq3x-(2-5x)

$$4 ( x + 2 ) \leq 3 x - ( 2 - 5 x )$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 4 by x+2.

$$4x+8\leq 3x-\left(2-5x\right)$$

To find the opposite of 2-5x, find the opposite of each term.

$$4x+8\leq 3x-2-\left(-5x\right)$$

The opposite of -5x is 5x.

$$4x+8\leq 3x-2+5x$$

Combine 3x and 5x to get 8x.

$$4x+8\leq 8x-2$$

Subtract 8x from both sides.

$$4x+8-8x\leq -2$$

Combine 4x and -8x to get -4x.

$$-4x+8\leq -2$$

Subtract 8 from both sides.

$$-4x\leq -2-8$$

Subtract 8 from -2 to get -10.

$$-4x\leq -10$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\geq \frac{-10}{-4}$$

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

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