Solve 148/111=128+x/58.5

$$\frac { 148 } { 111 } = \frac { 128 + x } { 58.5 }$$

Solve for x

$$x=-50$$

Steps for Solving Linear Equation

Reduce the fraction \frac{148}{111} to lowest terms by extracting and canceling out 37.

$$\frac{4}{3}=\frac{128+x}{58.5}$$

Divide each term of 128+x by 58.5 to get \frac{128}{58.5}+\frac{x}{58.5}.

$$\frac{4}{3}=\frac{128}{58.5}+\frac{x}{58.5}$$

Expand \frac{128}{58.5} by multiplying both numerator and the denominator by 10.

$$\frac{4}{3}=\frac{1280}{585}+\frac{x}{58.5}$$

Reduce the fraction \frac{1280}{585} to lowest terms by extracting and canceling out 5.

$$\frac{4}{3}=\frac{256}{117}+\frac{x}{58.5}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{256}{117}+\frac{x}{58.5}=\frac{4}{3}$$

Subtract \frac{256}{117} from both sides.

$$\frac{x}{58.5}=\frac{4}{3}-\frac{256}{117}$$

Least common multiple of 3 and 117 is 117. Convert \frac{4}{3} and \frac{256}{117} to fractions with denominator 117.

$$\frac{x}{58.5}=\frac{156}{117}-\frac{256}{117}$$

Since \frac{156}{117} and \frac{256}{117} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{58.5}=\frac{156-256}{117}$$

Subtract 256 from 156 to get -100.

$$\frac{x}{58.5}=-\frac{100}{117}$$

Multiply both sides by 58.5.

$$x=-\frac{100}{117}\times 58.5$$

Convert decimal number 58.5 to fraction \frac{585}{10}. Reduce the fraction \frac{585}{10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{100}{117}\times \frac{117}{2}$$

Multiply -\frac{100}{117} times \frac{117}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-100\times 117}{117\times 2}$$

Cancel out 117 in both numerator and denominator.

$$x=\frac{-100}{2}$$

Divide -100 by 2 to get -50.

$$x=-50$$