Solve 2/3(x-3)=1/4(x+7)

$$\frac { 2 } { 3 } ( x - 3 ) = \frac { 1 } { 4 } ( x + 7 )$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}x+\frac{2}{3}\left(-3\right)=\frac{1}{4}\left(x+7\right)$$

Express \frac{2}{3}\left(-3\right) as a single fraction.

$$\frac{2}{3}x+\frac{2\left(-3\right)}{3}=\frac{1}{4}\left(x+7\right)$$

Multiply 2 and -3 to get -6.

$$\frac{2}{3}x+\frac{-6}{3}=\frac{1}{4}\left(x+7\right)$$

Divide -6 by 3 to get -2.

$$\frac{2}{3}x-2=\frac{1}{4}\left(x+7\right)$$

Use the distributive property to multiply \frac{1}{4} by x+7.

$$\frac{2}{3}x-2=\frac{1}{4}x+\frac{1}{4}\times 7$$

Multiply \frac{1}{4} and 7 to get \frac{7}{4}.

$$\frac{2}{3}x-2=\frac{1}{4}x+\frac{7}{4}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{2}{3}x-2-\frac{1}{4}x=\frac{7}{4}$$

Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.

$$\frac{5}{12}x-2=\frac{7}{4}$$

Add 2 to both sides.

$$\frac{5}{12}x=\frac{7}{4}+2$$

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

$$\frac{5}{12}x=\frac{7}{4}+\frac{8}{4}$$

Since \frac{7}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{7+8}{4}$$

Add 7 and 8 to get 15.

$$\frac{5}{12}x=\frac{15}{4}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=\frac{15}{4}\times \frac{12}{5}$$

Multiply \frac{15}{4} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{15\times 12}{4\times 5}$$

Do the multiplications in the fraction \frac{15\times 12}{4\times 5}.

$$x=\frac{180}{20}$$

Divide 180 by 20 to get 9.

$$x=9$$