Solve 5x+2/3+5leq2x+3

$$\frac{ 5x+2 }{ 3 } +5 \leq 2x+3$$

Solve for x

$$x\geq 8$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$5x+2+15\leq 6x+9$$

Add 2 and 15 to get 17.

$$5x+17\leq 6x+9$$

Subtract 6x from both sides.

$$5x+17-6x\leq 9$$

Combine 5x and -6x to get -x.

$$-x+17\leq 9$$

Subtract 17 from both sides.

$$-x\leq 9-17$$

Subtract 17 from 9 to get -8.

$$-x\leq -8$$

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

$$x\geq \frac{-8}{-1}$$

Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.

$$x\geq 8$$