Solve 2/3(x+2)+7=4/9(3x-7)

$$\frac { 2 } { 3 } ( x + 2 ) + 7 = \frac { 4 } { 9 } ( 3 x - 7 )$$

Solve for x

$$x = \frac{103}{6} = 17\frac{1}{6} \approx 17.166666667$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}x+\frac{2}{3}\times 2+7=\frac{4}{9}\left(3x-7\right)$$

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

$$\frac{2}{3}x+\frac{2\times 2}{3}+7=\frac{4}{9}\left(3x-7\right)$$

Multiply 2 and 2 to get 4.

$$\frac{2}{3}x+\frac{4}{3}+7=\frac{4}{9}\left(3x-7\right)$$

Convert 7 to fraction \frac{21}{3}.

$$\frac{2}{3}x+\frac{4}{3}+\frac{21}{3}=\frac{4}{9}\left(3x-7\right)$$

Since \frac{4}{3} and \frac{21}{3} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}x+\frac{4+21}{3}=\frac{4}{9}\left(3x-7\right)$$

Add 4 and 21 to get 25.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{9}\left(3x-7\right)$$

Use the distributive property to multiply \frac{4}{9} by 3x-7.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{9}\times 3x+\frac{4}{9}\left(-7\right)$$

Express \frac{4}{9}\times 3 as a single fraction.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4\times 3}{9}x+\frac{4}{9}\left(-7\right)$$

Multiply 4 and 3 to get 12.

$$\frac{2}{3}x+\frac{25}{3}=\frac{12}{9}x+\frac{4}{9}\left(-7\right)$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{3}x+\frac{4}{9}\left(-7\right)$$

Express \frac{4}{9}\left(-7\right) as a single fraction.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{3}x+\frac{4\left(-7\right)}{9}$$

Multiply 4 and -7 to get -28.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{3}x+\frac{-28}{9}$$

Fraction \frac{-28}{9} can be rewritten as -\frac{28}{9} by extracting the negative sign.

$$\frac{2}{3}x+\frac{25}{3}=\frac{4}{3}x-\frac{28}{9}$$

Subtract \frac{4}{3}x from both sides.

$$\frac{2}{3}x+\frac{25}{3}-\frac{4}{3}x=-\frac{28}{9}$$

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

$$-\frac{2}{3}x+\frac{25}{3}=-\frac{28}{9}$$

Subtract \frac{25}{3} from both sides.

$$-\frac{2}{3}x=-\frac{28}{9}-\frac{25}{3}$$

Least common multiple of 9 and 3 is 9. Convert -\frac{28}{9} and \frac{25}{3} to fractions with denominator 9.

$$-\frac{2}{3}x=-\frac{28}{9}-\frac{75}{9}$$

Since -\frac{28}{9} and \frac{75}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x=\frac{-28-75}{9}$$

Subtract 75 from -28 to get -103.

$$-\frac{2}{3}x=-\frac{103}{9}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x=-\frac{103}{9}\left(-\frac{3}{2}\right)$$

Multiply -\frac{103}{9} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-103\left(-3\right)}{9\times 2}$$

Do the multiplications in the fraction \frac{-103\left(-3\right)}{9\times 2}.

$$x=\frac{309}{18}$$

Reduce the fraction \frac{309}{18} to lowest terms by extracting and canceling out 3.

$$x=\frac{103}{6}$$