Solve x-13=7/10(x+5)

$$x - 13 = \frac { 7 } { 10 } ( x + 5 )$$

Solve for x

$$x=55$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{10} by x+5.

$$x-13=\frac{7}{10}x+\frac{7}{10}\times 5$$

Express \frac{7}{10}\times 5 as a single fraction.

$$x-13=\frac{7}{10}x+\frac{7\times 5}{10}$$

Multiply 7 and 5 to get 35.

$$x-13=\frac{7}{10}x+\frac{35}{10}$$

Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$x-13=\frac{7}{10}x+\frac{7}{2}$$

Subtract \frac{7}{10}x from both sides.

$$x-13-\frac{7}{10}x=\frac{7}{2}$$

Combine x and -\frac{7}{10}x to get \frac{3}{10}x.

$$\frac{3}{10}x-13=\frac{7}{2}$$

Add 13 to both sides.

$$\frac{3}{10}x=\frac{7}{2}+13$$

Convert 13 to fraction \frac{26}{2}.

$$\frac{3}{10}x=\frac{7}{2}+\frac{26}{2}$$

Since \frac{7}{2} and \frac{26}{2} have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x=\frac{7+26}{2}$$

Add 7 and 26 to get 33.

$$\frac{3}{10}x=\frac{33}{2}$$

Multiply both sides by \frac{10}{3}, the reciprocal of \frac{3}{10}.

$$x=\frac{33}{2}\times \frac{10}{3}$$

Multiply \frac{33}{2} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{33\times 10}{2\times 3}$$

Do the multiplications in the fraction \frac{33\times 10}{2\times 3}.

$$x=\frac{330}{6}$$

Divide 330 by 6 to get 55.

$$x=55$$