Solve (1/3x-2x)*5/2+2=x+1/4

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

Solve for x

$$x=\frac{21}{62}\approx 0.338709677$$

Steps for Solving Linear Equation

Combine \frac{1}{3}x and -2x to get -\frac{5}{3}x.

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

Multiply -\frac{5}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5\times 5}{3\times 2}.

$$\frac{-25}{6}x+2=x+\frac{1}{4}$$

Fraction \frac{-25}{6} can be rewritten as -\frac{25}{6} by extracting the negative sign.

$$-\frac{25}{6}x+2=x+\frac{1}{4}$$

Subtract x from both sides.

$$-\frac{25}{6}x+2-x=\frac{1}{4}$$

Combine -\frac{25}{6}x and -x to get -\frac{31}{6}x.

$$-\frac{31}{6}x+2=\frac{1}{4}$$

Subtract 2 from both sides.

$$-\frac{31}{6}x=\frac{1}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{31}{6}x=\frac{1}{4}-\frac{8}{4}$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{31}{6}x=\frac{1-8}{4}$$

Subtract 8 from 1 to get -7.

$$-\frac{31}{6}x=-\frac{7}{4}$$

Multiply both sides by -\frac{6}{31}, the reciprocal of -\frac{31}{6}.

$$x=-\frac{7}{4}\left(-\frac{6}{31}\right)$$

Multiply -\frac{7}{4} times -\frac{6}{31} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-6\right)}{4\times 31}$$

Do the multiplications in the fraction \frac{-7\left(-6\right)}{4\times 31}.

$$x=\frac{42}{124}$$

Reduce the fraction \frac{42}{124} to lowest terms by extracting and canceling out 2.

$$x=\frac{21}{62}$$