Solve 4-3(x+1)/4geq5(x+2)/8+2

$$4- \frac{ 3(x+1) }{ 4 } \geq \frac{ 5(x+2) }{ 8 } +2$$

Solve for x

$$x\leq 0$$

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.

$$32-2\times 3\left(x+1\right)\geq 5\left(x+2\right)+16$$

Multiply -2 and 3 to get -6.

$$32-6\left(x+1\right)\geq 5\left(x+2\right)+16$$

Use the distributive property to multiply -6 by x+1.

$$32-6x-6\geq 5\left(x+2\right)+16$$

Subtract 6 from 32 to get 26.

$$26-6x\geq 5\left(x+2\right)+16$$

Use the distributive property to multiply 5 by x+2.

$$26-6x\geq 5x+10+16$$

Add 10 and 16 to get 26.

$$26-6x\geq 5x+26$$

Subtract 5x from both sides.

$$26-6x-5x\geq 26$$

Combine -6x and -5x to get -11x.

$$26-11x\geq 26$$

Subtract 26 from both sides.

$$-11x\geq 26-26$$

Subtract 26 from 26 to get 0.

$$-11x\geq 0$$

Product of two numbers is ≥0 if both are ≥0 or both are ≤0. Since -11\leq 0, x must be ≤0.

$$x\leq 0$$