Solve 1/2(x+1/4)=2/3x-1/6

$$\frac { 1 } { 2 } ( x + \frac { 1 } { 4 } ) = \frac { 2 } { 3 } x - \frac { 1 } { 6 }$$

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+\frac{1}{4}.

$$\frac{1}{2}x+\frac{1}{2}\times \frac{1}{4}=\frac{2}{3}x-\frac{1}{6}$$

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

$$\frac{1}{2}x+\frac{1\times 1}{2\times 4}=\frac{2}{3}x-\frac{1}{6}$$

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

$$\frac{1}{2}x+\frac{1}{8}=\frac{2}{3}x-\frac{1}{6}$$

Subtract \frac{2}{3}x from both sides.

$$\frac{1}{2}x+\frac{1}{8}-\frac{2}{3}x=-\frac{1}{6}$$

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x+\frac{1}{8}=-\frac{1}{6}$$

Subtract \frac{1}{8} from both sides.

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

Least common multiple of 6 and 8 is 24. Convert -\frac{1}{6} and \frac{1}{8} to fractions with denominator 24.

$$-\frac{1}{6}x=-\frac{4}{24}-\frac{3}{24}$$

Since -\frac{4}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}x=\frac{-4-3}{24}$$

Subtract 3 from -4 to get -7.

$$-\frac{1}{6}x=-\frac{7}{24}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=-\frac{7}{24}\left(-6\right)$$

Express -\frac{7}{24}\left(-6\right) as a single fraction.

$$x=\frac{-7\left(-6\right)}{24}$$

Multiply -7 and -6 to get 42.

$$x=\frac{42}{24}$$

Reduce the fraction \frac{42}{24} to lowest terms by extracting and canceling out 6.

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