Solve 2x-1/3leq3x-4/4

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

Solve for x

$$x\geq 8$$

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.

$$4\left(2x-1\right)\leq 3\left(3x-4\right)$$

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

$$8x-4\leq 3\left(3x-4\right)$$

Use the distributive property to multiply 3 by 3x-4.

$$8x-4\leq 9x-12$$

Subtract 9x from both sides.

$$8x-4-9x\leq -12$$

Combine 8x and -9x to get -x.

$$-x-4\leq -12$$

Add 4 to both sides.

$$-x\leq -12+4$$

Add -12 and 4 to get -8.

$$-x\leq -8$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-8}{-1}$$

Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.

$$x\geq 8$$