Solve 3x/4geqx-1/5

$$\frac { 3 x } { 4 } \geq \frac { x - 1 } { 5 }$$

Solve for x

$$x\geq -\frac{4}{11}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,5. Since 20 is positive, the inequality direction remains the same.

$$5\times 3x\geq 4\left(x-1\right)$$

Multiply 5 and 3 to get 15.

$$15x\geq 4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

$$15x\geq 4x-4$$

Subtract 4x from both sides.

$$15x-4x\geq -4$$

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

$$11x\geq -4$$

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

$$x\geq -\frac{4}{11}$$