Solve x+4/3-2/3leq4/5-3-2x/16

$$\frac{ x+4 }{ 3 } - \frac{ 2 }{ 3 } \leq \frac{ 4 }{ 5 } - \frac{ 3-2x }{ 16 }$$

Solve for x

$$x\leq -\frac{13}{50}$$

Solution Steps

Multiply both sides of the equation by 240, the least common multiple of 3,5,16. Since 240 is positive, the inequality direction remains the same.

$$80\left(x+4\right)-160\leq 192-15\left(3-2x\right)$$

Use the distributive property to multiply 80 by x+4.

$$80x+320-160\leq 192-15\left(3-2x\right)$$

Subtract 160 from 320 to get 160.

$$80x+160\leq 192-15\left(3-2x\right)$$

Use the distributive property to multiply -15 by 3-2x.

$$80x+160\leq 192-45+30x$$

Subtract 45 from 192 to get 147.

$$80x+160\leq 147+30x$$

Subtract 30x from both sides.

$$80x+160-30x\leq 147$$

Combine 80x and -30x to get 50x.

$$50x+160\leq 147$$

Subtract 160 from both sides.

$$50x\leq 147-160$$

Subtract 160 from 147 to get -13.

$$50x\leq -13$$

Divide both sides by 50. Since 50 is positive, the inequality direction remains the same.

$$x\leq -\frac{13}{50}$$