Solve 4-x/5+x+1/6geq2

$$\frac { 4 - x } { 5 } + \frac { x + 1 } { 6 } \geq 2$$

Solve for x

$$x\leq -31$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,6. Since 30 is positive, the inequality direction remains the same.

$$6\left(4-x\right)+5\left(x+1\right)\geq 60$$

Use the distributive property to multiply 6 by 4-x.

$$24-6x+5\left(x+1\right)\geq 60$$

Use the distributive property to multiply 5 by x+1.

$$24-6x+5x+5\geq 60$$

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

$$24-x+5\geq 60$$

Add 24 and 5 to get 29.

$$29-x\geq 60$$

Subtract 29 from both sides.

$$-x\geq 60-29$$

Subtract 29 from 60 to get 31.

$$-x\geq 31$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq -31$$