Solve x-7/5-3-2x/6geq2

$$\frac { x - 7 } { 5 } - \frac { 3 - 2 x } { 6 } \geq 2$$

Solve for x

$$x\geq \frac{117}{16}$$

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.

$$6\left(x-7\right)-5\left(3-2x\right)\geq 60$$

Use the distributive property to multiply 6 by x-7.

$$6x-42-5\left(3-2x\right)\geq 60$$

Use the distributive property to multiply -5 by 3-2x.

$$6x-42-15+10x\geq 60$$

Subtract 15 from -42 to get -57.

$$6x-57+10x\geq 60$$

Combine 6x and 10x to get 16x.

$$16x-57\geq 60$$

Add 57 to both sides.

$$16x\geq 60+57$$

Add 60 and 57 to get 117.

$$16x\geq 117$$

Divide both sides by 16. Since 16 is positive, the inequality direction remains the same.

$$x\geq \frac{117}{16}$$