Solve x+1/3leq3+5x-1/2

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

Solve for x

$$x\geq -1$$

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.

$$2\left(x+1\right)\leq 18+3\left(5x-1\right)$$

Use the distributive property to multiply 2 by x+1.

$$2x+2\leq 18+3\left(5x-1\right)$$

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

$$2x+2\leq 18+15x-3$$

Subtract 3 from 18 to get 15.

$$2x+2\leq 15+15x$$

Subtract 15x from both sides.

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

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

$$-13x+2\leq 15$$

Subtract 2 from both sides.

$$-13x\leq 15-2$$

Subtract 2 from 15 to get 13.

$$-13x\leq 13$$

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

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

Divide 13 by -13 to get -1.

$$x\geq -1$$