Solve 3x+2/4-3leq9x+1/8

$$\frac { 3 x + 2 } { 4 } - 3 \leq \frac { 9 x + 1 } { 8 }$$

Solve for x

$$x\geq -7$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,8. Since 8 is positive, the inequality direction remains the same.

$$2\left(3x+2\right)-24\leq 9x+1$$

Use the distributive property to multiply 2 by 3x+2.

$$6x+4-24\leq 9x+1$$

Subtract 24 from 4 to get -20.

$$6x-20\leq 9x+1$$

Subtract 9x from both sides.

$$6x-20-9x\leq 1$$

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

$$-3x-20\leq 1$$

Add 20 to both sides.

$$-3x\leq 1+20$$

Add 1 and 20 to get 21.

$$-3x\leq 21$$

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

$$x\geq \frac{21}{-3}$$

Divide 21 by -3 to get -7.

$$x\geq -7$$