Solve 2x-3/4-x-4/3geq1

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

Solve for x

$$x\geq \frac{5}{2}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(2x-3\right)-4\left(x-4\right)\geq 12$$

Use the distributive property to multiply 3 by 2x-3.

$$6x-9-4\left(x-4\right)\geq 12$$

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

$$6x-9-4x+16\geq 12$$

Combine 6x and -4x to get 2x.

$$2x-9+16\geq 12$$

Add -9 and 16 to get 7.

$$2x+7\geq 12$$

Subtract 7 from both sides.

$$2x\geq 12-7$$

Subtract 7 from 12 to get 5.

$$2x\geq 5$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\geq \frac{5}{2}$$