Solve 4(x+2)/3-6(x-7)/7geq12

$$\frac { 4 ( x + 2 ) } { 3 } - \frac { 6 ( x - 7 ) } { 7 } \geq 12$$

Solve for x

$$x\geq 7$$

Solution Steps

Multiply both sides of the equation by 21, the least common multiple of 3,7. Since 21 is positive, the inequality direction remains the same.

$$7\times 4\left(x+2\right)-3\times 6\left(x-7\right)\geq 252$$

Multiply 7 and 4 to get 28.

$$28\left(x+2\right)-3\times 6\left(x-7\right)\geq 252$$

Use the distributive property to multiply 28 by x+2.

$$28x+56-3\times 6\left(x-7\right)\geq 252$$

Multiply -3 and 6 to get -18.

$$28x+56-18\left(x-7\right)\geq 252$$

Use the distributive property to multiply -18 by x-7.

$$28x+56-18x+126\geq 252$$

Combine 28x and -18x to get 10x.

$$10x+56+126\geq 252$$

Add 56 and 126 to get 182.

$$10x+182\geq 252$$

Subtract 182 from both sides.

$$10x\geq 252-182$$

Subtract 182 from 252 to get 70.

$$10x\geq 70$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x\geq \frac{70}{10}$$

Divide 70 by 10 to get 7.

$$x\geq 7$$