Solve 2/3(x+7)-x/4leq1/2(3-x)+x/6

$$\frac{ 2 }{ 3 } (x+7)- \frac{ x }{ 4 } \leq \frac{ 1 }{ 2 } (3-x)+ \frac{ x }{ 6 }$$

Solve for x

$$x\leq -\frac{38}{9}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4,2,6. Since 12 is positive, the inequality direction remains the same.

$$8\left(x+7\right)-3x\leq 6\left(3-x\right)+2x$$

Use the distributive property to multiply 8 by x+7.

$$8x+56-3x\leq 6\left(3-x\right)+2x$$

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

$$5x+56\leq 6\left(3-x\right)+2x$$

Use the distributive property to multiply 6 by 3-x.

$$5x+56\leq 18-6x+2x$$

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

$$5x+56\leq 18-4x$$

Add 4x to both sides.

$$5x+56+4x\leq 18$$

Combine 5x and 4x to get 9x.

$$9x+56\leq 18$$

Subtract 56 from both sides.

$$9x\leq 18-56$$

Subtract 56 from 18 to get -38.

$$9x\leq -38$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x\leq -\frac{38}{9}$$