Solve =2x-1/3-5x+1/2leq1

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

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.

$$2\left(2x-1\right)-3\left(5x+1\right)\leq 6$$

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

$$4x-2-3\left(5x+1\right)\leq 6$$

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

$$4x-2-15x-3\leq 6$$

Combine 4x and -15x to get -11x.

$$-11x-2-3\leq 6$$

Subtract 3 from -2 to get -5.

$$-11x-5\leq 6$$

Add 5 to both sides.

$$-11x\leq 6+5$$

Add 6 and 5 to get 11.

$$-11x\leq 11$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x\geq \frac{11}{-11}$$

Divide 11 by -11 to get -1.

$$x\geq -1$$