Solve x+2/3leq5x+1/2

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

Solve for x

$$x\geq \frac{1}{13}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(x+2\right)\leq 3\left(5x+1\right)$$

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

$$2x+4\leq 3\left(5x+1\right)$$

Use the distributive property to multiply 3 by 5x+1.

$$2x+4\leq 15x+3$$

Subtract 15x from both sides.

$$2x+4-15x\leq 3$$

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

$$-13x+4\leq 3$$

Subtract 4 from both sides.

$$-13x\leq 3-4$$

Subtract 4 from 3 to get -1.

$$-13x\leq -1$$

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

$$x\geq \frac{-1}{-13}$$

Fraction \frac{-1}{-13} can be simplified to \frac{1}{13} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{13}$$