Solve 2x-1/3geq5/4x-5

$$\frac { 2 x - 1 } { 3 } \geq \frac { 5 } { 4 } x - 5$$

Solve for x

$$x\leq 8$$

Solution Steps

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

$$4\left(2x-1\right)\geq 15x-60$$

Use the distributive property to multiply 4 by 2x-1.

$$8x-4\geq 15x-60$$

Subtract 15x from both sides.

$$8x-4-15x\geq -60$$

Combine 8x and -15x to get -7x.

$$-7x-4\geq -60$$

Add 4 to both sides.

$$-7x\geq -60+4$$

Add -60 and 4 to get -56.

$$-7x\geq -56$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\leq \frac{-56}{-7}$$

Divide -56 by -7 to get 8.

$$x\leq 8$$