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

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

Solve for x

$$x=-\frac{20}{39}\approx -0.512820513$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4}x+\frac{1}{3} by \frac{1}{2}.

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

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

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

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

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

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

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

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

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

Subtract 2x from both sides.

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

Combine \frac{3}{8}x and -2x to get -\frac{13}{8}x.

$$-\frac{13}{8}x+\frac{1}{6}=1$$

Subtract \frac{1}{6} from both sides.

$$-\frac{13}{8}x=1-\frac{1}{6}$$

Convert 1 to fraction \frac{6}{6}.

$$-\frac{13}{8}x=\frac{6}{6}-\frac{1}{6}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{8}x=\frac{6-1}{6}$$

Subtract 1 from 6 to get 5.

$$-\frac{13}{8}x=\frac{5}{6}$$

Multiply both sides by -\frac{8}{13}, the reciprocal of -\frac{13}{8}.

$$x=\frac{5}{6}\left(-\frac{8}{13}\right)$$

Multiply \frac{5}{6} times -\frac{8}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\left(-8\right)}{6\times 13}$$

Do the multiplications in the fraction \frac{5\left(-8\right)}{6\times 13}.

$$x=\frac{-40}{78}$$

Reduce the fraction \frac{-40}{78} to lowest terms by extracting and canceling out 2.

$$x=-\frac{20}{39}$$