Solve x+3/2-1leq3x/4+5/6

$$\frac{ x+3 }{ 2 } -1 \leq \frac{ 3x }{ 4 } + \frac{ 5 }{ 6 }$$

Solve for x

$$x\geq -\frac{4}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,4,6. Since 12 is positive, the inequality direction remains the same.

$$6\left(x+3\right)-12\leq 3\times 3x+10$$

Use the distributive property to multiply 6 by x+3.

$$6x+18-12\leq 3\times 3x+10$$

Subtract 12 from 18 to get 6.

$$6x+6\leq 3\times 3x+10$$

Multiply 3 and 3 to get 9.

$$6x+6\leq 9x+10$$

Subtract 9x from both sides.

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

Combine 6x and -9x to get -3x.

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

Subtract 6 from both sides.

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

Subtract 6 from 10 to get 4.

$$-3x\leq 4$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\geq -\frac{4}{3}$$