Solve 1+2x/3leq5x-23/3

$$1 + \frac { 2 x } { 3 } \leq 5 x - \frac { 23 } { 3 }$$

Solve for x

$$x\geq 2$$

Solution Steps

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

$$3+2x\leq 15x-23$$

Subtract 15x from both sides.

$$3+2x-15x\leq -23$$

Combine 2x and -15x to get -13x.

$$3-13x\leq -23$$

Subtract 3 from both sides.

$$-13x\leq -23-3$$

Subtract 3 from -23 to get -26.

$$-13x\leq -26$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq \frac{-26}{-13}$$

Divide -26 by -13 to get 2.

$$x\geq 2$$