Solve 5x/3-1leq3x-1/2

$$\frac { 5 x } { 3 } - 1 \leq \frac { 3 x - 1 } { 2 }$$

Solve for x

$$x\leq 3$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\times 5x-6\leq 3\left(3x-1\right)$$

Multiply 2 and 5 to get 10.

$$10x-6\leq 3\left(3x-1\right)$$

Use the distributive property to multiply 3 by 3x-1.

$$10x-6\leq 9x-3$$

Subtract 9x from both sides.

$$10x-6-9x\leq -3$$

Combine 10x and -9x to get x.

$$x-6\leq -3$$

Add 6 to both sides.

$$x\leq -3+6$$

Add -3 and 6 to get 3.

$$x\leq 3$$