Solve 2x-1/3leq3x-4/6

$$\frac { 2 x - 1 } { 3 } \leq \frac { 3 x - 4 } { 6 }$$

Solve for x

$$x\leq -2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

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

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

$$4x-2\leq 3x-4$$

Subtract 3x from both sides.

$$4x-2-3x\leq -4$$

Combine 4x and -3x to get x.

$$x-2\leq -4$$

Add 2 to both sides.

$$x\leq -4+2$$

Add -4 and 2 to get -2.

$$x\leq -2$$