Solve 3x/3-4x+2/6leq3left(x+1right)

$$\frac{ 3x }{ 3 } - \frac{ 4x+2 }{ 6 } \leq 3 \left( x+1 \right)$$

Solve for x

$$x\geq -\frac{5}{4}$$

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.

$$2\times 3x-\left(4x+2\right)\leq 18\left(x+1\right)$$

Multiply 2 and 3 to get 6.

$$6x-\left(4x+2\right)\leq 18\left(x+1\right)$$

To find the opposite of 4x+2, find the opposite of each term.

$$6x-4x-2\leq 18\left(x+1\right)$$

Combine 6x and -4x to get 2x.

$$2x-2\leq 18\left(x+1\right)$$

Use the distributive property to multiply 18 by x+1.

$$2x-2\leq 18x+18$$

Subtract 18x from both sides.

$$2x-2-18x\leq 18$$

Combine 2x and -18x to get -16x.

$$-16x-2\leq 18$$

Add 2 to both sides.

$$-16x\leq 18+2$$

Add 18 and 2 to get 20.

$$-16x\leq 20$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\geq \frac{20}{-16}$$

Reduce the fraction \frac{20}{-16} to lowest terms by extracting and canceling out 4.

$$x\geq -\frac{5}{4}$$