Solve x+2/5-3(x-1)/2=x+7

$$\frac { x + 2 } { 5 } - \frac { 3 ( x - 1 ) } { 2 } = x + 7$$

Solve for x

$$x = -\frac{51}{23} = -2\frac{5}{23} \approx -2.217391304$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$2\left(x+2\right)-5\times 3\left(x-1\right)=10x+70$$

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

$$2x+4-5\times 3\left(x-1\right)=10x+70$$

Multiply -5 and 3 to get -15.

$$2x+4-15\left(x-1\right)=10x+70$$

Use the distributive property to multiply -15 by x-1.

$$2x+4-15x+15=10x+70$$

Combine 2x and -15x to get -13x.

$$-13x+4+15=10x+70$$

Add 4 and 15 to get 19.

$$-13x+19=10x+70$$

Subtract 10x from both sides.

$$-13x+19-10x=70$$

Combine -13x and -10x to get -23x.

$$-23x+19=70$$

Subtract 19 from both sides.

$$-23x=70-19$$

Subtract 19 from 70 to get 51.

$$-23x=51$$

Divide both sides by -23.

$$x=\frac{51}{-23}$$

Fraction \frac{51}{-23} can be rewritten as -\frac{51}{23} by extracting the negative sign.

$$x=-\frac{51}{23}$$