Solve 5x+1/2geq2x-1/3

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

Solve for x

$$x\geq -\frac{5}{11}$$

Solution Steps

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

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

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

$$15x+3\geq 2\left(2x-1\right)$$

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

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

Subtract 4x from both sides.

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

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

$$11x+3\geq -2$$

Subtract 3 from both sides.

$$11x\geq -2-3$$

Subtract 3 from -2 to get -5.

$$11x\geq -5$$

Divide both sides by 11. Since 11 is positive, the inequality direction remains the same.

$$x\geq -\frac{5}{11}$$