Solve x/2+x/6leq7+x/1

$$\frac { x } { 2 } + \frac { x } { 6 } \leq 7 + \frac { x } { 1 }$$

Solve for x

$$x\geq -21$$

Solution Steps

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

$$3x+x\leq 42+6x$$

Combine 3x and x to get 4x.

$$4x\leq 42+6x$$

Subtract 6x from both sides.

$$4x-6x\leq 42$$

Combine 4x and -6x to get -2x.

$$-2x\leq 42$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\geq \frac{42}{-2}$$

Divide 42 by -2 to get -21.

$$x\geq -21$$