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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 5x+4.

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

Express \frac{2}{3}\times 5 as a single fraction.

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

Multiply 2 and 5 to get 10.

$$\frac{10}{3}x+\frac{2}{3}\times 4=\frac{1}{2}\left(3x-4\right)+1$$

Express \frac{2}{3}\times 4 as a single fraction.

$$\frac{10}{3}x+\frac{2\times 4}{3}=\frac{1}{2}\left(3x-4\right)+1$$

Multiply 2 and 4 to get 8.

$$\frac{10}{3}x+\frac{8}{3}=\frac{1}{2}\left(3x-4\right)+1$$

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

$$\frac{10}{3}x+\frac{8}{3}=\frac{1}{2}\times 3x+\frac{1}{2}\left(-4\right)+1$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{10}{3}x+\frac{8}{3}=\frac{3}{2}x+\frac{1}{2}\left(-4\right)+1$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$\frac{10}{3}x+\frac{8}{3}=\frac{3}{2}x+\frac{-4}{2}+1$$

Divide -4 by 2 to get -2.

$$\frac{10}{3}x+\frac{8}{3}=\frac{3}{2}x-2+1$$

Add -2 and 1 to get -1.

$$\frac{10}{3}x+\frac{8}{3}=\frac{3}{2}x-1$$

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

$$\frac{10}{3}x+\frac{8}{3}-\frac{3}{2}x=-1$$

Combine \frac{10}{3}x and -\frac{3}{2}x to get \frac{11}{6}x.

$$\frac{11}{6}x+\frac{8}{3}=-1$$

Subtract \frac{8}{3} from both sides.

$$\frac{11}{6}x=-1-\frac{8}{3}$$

Convert -1 to fraction -\frac{3}{3}.

$$\frac{11}{6}x=-\frac{3}{3}-\frac{8}{3}$$

Since -\frac{3}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{6}x=\frac{-3-8}{3}$$

Subtract 8 from -3 to get -11.

$$\frac{11}{6}x=-\frac{11}{3}$$

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

$$x=-\frac{11}{3}\times \frac{6}{11}$$

Multiply -\frac{11}{3} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\times 6}{3\times 11}$$

Do the multiplications in the fraction \frac{-11\times 6}{3\times 11}.

$$x=\frac{-66}{33}$$

Divide -66 by 33 to get -2.

$$x=-2$$