Solve 0.5-3/4=9/4x+x

$$0.5 - \frac { 3 } { 4 } = \frac { 9 } { 4 } x + x$$

Solve for x

$$x=-\frac{1}{13}\approx -0.076923077$$

Steps for Solving Linear Equation

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}-\frac{3}{4}=\frac{9}{4}x+x$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}-\frac{3}{4}=\frac{9}{4}x+x$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{4}=\frac{9}{4}x+x$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{4}=\frac{9}{4}x+x$$

Combine \frac{9}{4}x and x to get \frac{13}{4}x.

$$-\frac{1}{4}=\frac{13}{4}x$$

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

$$\frac{13}{4}x=-\frac{1}{4}$$

Multiply both sides by \frac{4}{13}, the reciprocal of \frac{13}{4}.

$$x=-\frac{1}{4}\times \frac{4}{13}$$

Multiply -\frac{1}{4} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-4}{4\times 13}$$

Cancel out 4 in both numerator and denominator.

$$x=\frac{-1}{13}$$

Fraction \frac{-1}{13} can be rewritten as -\frac{1}{13} by extracting the negative sign.

$$x=-\frac{1}{13}$$