Solve x/3=x+5/1-5+10

$$\frac { x } { 3 } = \frac { x + 5 } { 1 - 5 } + 10$$

Solve for x

$$x=15$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$x=-\frac{3}{4}\left(x+5\right)+30$$

Use the distributive property to multiply -\frac{3}{4} by x+5.

$$x=-\frac{3}{4}x-\frac{3}{4}\times 5+30$$

Express -\frac{3}{4}\times 5 as a single fraction.

$$x=-\frac{3}{4}x+\frac{-3\times 5}{4}+30$$

Multiply -3 and 5 to get -15.

$$x=-\frac{3}{4}x+\frac{-15}{4}+30$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$x=-\frac{3}{4}x-\frac{15}{4}+30$$

Convert 30 to fraction \frac{120}{4}.

$$x=-\frac{3}{4}x-\frac{15}{4}+\frac{120}{4}$$

Since -\frac{15}{4} and \frac{120}{4} have the same denominator, add them by adding their numerators.

$$x=-\frac{3}{4}x+\frac{-15+120}{4}$$

Add -15 and 120 to get 105.

$$x=-\frac{3}{4}x+\frac{105}{4}$$

Add \frac{3}{4}x to both sides.

$$x+\frac{3}{4}x=\frac{105}{4}$$

Combine x and \frac{3}{4}x to get \frac{7}{4}x.

$$\frac{7}{4}x=\frac{105}{4}$$

Multiply both sides by \frac{4}{7}, the reciprocal of \frac{7}{4}.

$$x=\frac{105}{4}\times \frac{4}{7}$$

Multiply \frac{105}{4} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{105\times 4}{4\times 7}$$

Cancel out 4 in both numerator and denominator.

$$x=\frac{105}{7}$$

Divide 105 by 7 to get 15.

$$x=15$$