Solve 4(1+x)/3-1leq5+x/2

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

Solve for x

$$x\leq \frac{13}{5}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\times 4\left(1+x\right)-6\leq 3\left(5+x\right)$$

Multiply 2 and 4 to get 8.

$$8\left(1+x\right)-6\leq 3\left(5+x\right)$$

Use the distributive property to multiply 8 by 1+x.

$$8+8x-6\leq 3\left(5+x\right)$$

Subtract 6 from 8 to get 2.

$$2+8x\leq 3\left(5+x\right)$$

Use the distributive property to multiply 3 by 5+x.

$$2+8x\leq 15+3x$$

Subtract 3x from both sides.

$$2+8x-3x\leq 15$$

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

$$2+5x\leq 15$$

Subtract 2 from both sides.

$$5x\leq 15-2$$

Subtract 2 from 15 to get 13.

$$5x\leq 13$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\leq \frac{13}{5}$$