Solve 1/23/4-5/2/-2=frac{1}{4}x

$$\frac{ 1 }{ 2 } \frac{ 3 }{ 4 } - \frac{ \frac{ 5 }{ 2 } }{ -2 } = \frac{ 1 }{ 4 } x$$

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 4}-\frac{\frac{5}{2}}{-2}=\frac{1}{4}x$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{3}{8}-\frac{\frac{5}{2}}{-2}=\frac{1}{4}x$$

Express \frac{\frac{5}{2}}{-2} as a single fraction.

$$\frac{3}{8}-\frac{5}{2\left(-2\right)}=\frac{1}{4}x$$

Multiply 2 and -2 to get -4.

$$\frac{3}{8}-\frac{5}{-4}=\frac{1}{4}x$$

Fraction \frac{5}{-4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{3}{8}-\left(-\frac{5}{4}\right)=\frac{1}{4}x$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$\frac{3}{8}+\frac{5}{4}=\frac{1}{4}x$$

Least common multiple of 8 and 4 is 8. Convert \frac{3}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{3}{8}+\frac{10}{8}=\frac{1}{4}x$$

Since \frac{3}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{3+10}{8}=\frac{1}{4}x$$

Add 3 and 10 to get 13.

$$\frac{13}{8}=\frac{1}{4}x$$

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

$$\frac{1}{4}x=\frac{13}{8}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=\frac{13}{8}\times 4$$

Express \frac{13}{8}\times 4 as a single fraction.

$$x=\frac{13\times 4}{8}$$

Multiply 13 and 4 to get 52.

$$x=\frac{52}{8}$$

Reduce the fraction \frac{52}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{13}{2}$$