Solve 3(x-5/6)leqx+1/2

$$3 ( x - \frac { 5 } { 6 } ) \leq x + \frac { 1 } { 2 }$$

Solve for x

$$x\leq \frac{3}{2}$$

Solution Steps

Use the distributive property to multiply 3 by x-\frac{5}{6}.

$$3x+3\left(-\frac{5}{6}\right)\leq x+\frac{1}{2}$$

Express 3\left(-\frac{5}{6}\right) as a single fraction.

$$3x+\frac{3\left(-5\right)}{6}\leq x+\frac{1}{2}$$

Multiply 3 and -5 to get -15.

$$3x+\frac{-15}{6}\leq x+\frac{1}{2}$$

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

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

Subtract x from both sides.

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

Combine 3x and -x to get 2x.

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

Add \frac{5}{2} to both sides.

$$2x\leq \frac{1}{2}+\frac{5}{2}$$

Since \frac{1}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$2x\leq \frac{1+5}{2}$$

Add 1 and 5 to get 6.

$$2x\leq \frac{6}{2}$$

Divide 6 by 2 to get 3.

$$2x\leq 3$$

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

$$x\leq \frac{3}{2}$$