Solve 4-x/2-1geq4(x+1)/3

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

Solve for x

$$x\leq -\frac{2}{11}$$

Solution Steps

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

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

Use the distributive property to multiply 3 by 4-x.

$$12-3x-6\geq 2\times 4\left(x+1\right)$$

Subtract 6 from 12 to get 6.

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

Multiply 2 and 4 to get 8.

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

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

$$6-3x\geq 8x+8$$

Subtract 8x from both sides.

$$6-3x-8x\geq 8$$

Combine -3x and -8x to get -11x.

$$6-11x\geq 8$$

Subtract 6 from both sides.

$$-11x\geq 8-6$$

Subtract 6 from 8 to get 2.

$$-11x\geq 2$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x\leq -\frac{2}{11}$$