Solve 1x+7/2-5x-1/5=x+5

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

Solve for x

$$x=-\frac{13}{15}\approx -0.866666667$$

Steps for Solving Linear Equation

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

$$5\left(1x+7\right)-2\left(5x-1\right)=10x+50$$

Use the distributive property to multiply 5 by 1x+7.

$$5x+35-2\left(5x-1\right)=10x+50$$

Use the distributive property to multiply -2 by 5x-1.

$$5x+35-10x+2=10x+50$$

Combine 5x and -10x to get -5x.

$$-5x+35+2=10x+50$$

Add 35 and 2 to get 37.

$$-5x+37=10x+50$$

Subtract 10x from both sides.

$$-5x+37-10x=50$$

Combine -5x and -10x to get -15x.

$$-15x+37=50$$

Subtract 37 from both sides.

$$-15x=50-37$$

Subtract 37 from 50 to get 13.

$$-15x=13$$

Divide both sides by -15.

$$x=\frac{13}{-15}$$

Fraction \frac{13}{-15} can be rewritten as -\frac{13}{15} by extracting the negative sign.

$$x=-\frac{13}{15}$$