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

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

Solve for x

$$x\geq -\frac{20}{13}$$

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.

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

Multiply 2 and 4 to get 8.

$$8x-\left(3x+2\right)\leq 18\left(x+1\right)$$

To find the opposite of 3x+2, find the opposite of each term.

$$8x-3x-2\leq 18\left(x+1\right)$$

Combine 8x and -3x to get 5x.

$$5x-2\leq 18\left(x+1\right)$$

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

$$5x-2\leq 18x+18$$

Subtract 18x from both sides.

$$5x-2-18x\leq 18$$

Combine 5x and -18x to get -13x.

$$-13x-2\leq 18$$

Add 2 to both sides.

$$-13x\leq 18+2$$

Add 18 and 2 to get 20.

$$-13x\leq 20$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq -\frac{20}{13}$$