Solve 1/4+1+3-5/2=2/3x

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

Solve for x

$$x = \frac{21}{8} = 2\frac{5}{8} = 2.625$$

Steps for Solving Linear Equation

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

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

Convert 3 to fraction \frac{12}{4}.

$$\frac{5}{4}+\frac{12}{4}-\frac{5}{2}=\frac{2}{3}x$$

Since \frac{5}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{4}-\frac{5}{2}=\frac{2}{3}x$$

Add 5 and 12 to get 17.

$$\frac{17}{4}-\frac{5}{2}=\frac{2}{3}x$$

Least common multiple of 4 and 2 is 4. Convert \frac{17}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{17}{4}-\frac{10}{4}=\frac{2}{3}x$$

Since \frac{17}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-10}{4}=\frac{2}{3}x$$

Subtract 10 from 17 to get 7.

$$\frac{7}{4}=\frac{2}{3}x$$

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

$$\frac{2}{3}x=\frac{7}{4}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x=\frac{7}{4}\times \frac{3}{2}$$

Multiply \frac{7}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 3}{4\times 2}$$

Do the multiplications in the fraction \frac{7\times 3}{4\times 2}.

$$x=\frac{21}{8}$$