Solve 2x-1/4+3/2geqx/8

$$\frac { 2 x - 1 } { 4 } + \frac { 3 } { 2 } \geq \frac { x } { 8 }$$

Solve for x

$$x\geq -\frac{10}{3}$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,2,8. Since 8 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)+12\geq x$$

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

$$4x-2+12\geq x$$

Add -2 and 12 to get 10.

$$4x+10\geq x$$

Subtract x from both sides.

$$4x+10-x\geq 0$$

Combine 4x and -x to get 3x.

$$3x+10\geq 0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$3x\geq -10$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\geq -\frac{10}{3}$$