Solve 1/2(3x-5)=2/5(4x+9)

$$\frac { 1 } { 2 } ( 3 x - 5 ) = \frac { 2 } { 5 } ( 4 x + 9 )$$

Solve for x

$$x=-61$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 3x-5.

$$\frac{1}{2}\times 3x+\frac{1}{2}\left(-5\right)=\frac{2}{5}\left(4x+9\right)$$

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

$$\frac{3}{2}x+\frac{1}{2}\left(-5\right)=\frac{2}{5}\left(4x+9\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$\frac{3}{2}x+\frac{-5}{2}=\frac{2}{5}\left(4x+9\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{3}{2}x-\frac{5}{2}=\frac{2}{5}\left(4x+9\right)$$

Use the distributive property to multiply \frac{2}{5} by 4x+9.

$$\frac{3}{2}x-\frac{5}{2}=\frac{2}{5}\times 4x+\frac{2}{5}\times 9$$

Express \frac{2}{5}\times 4 as a single fraction.

$$\frac{3}{2}x-\frac{5}{2}=\frac{2\times 4}{5}x+\frac{2}{5}\times 9$$

Multiply 2 and 4 to get 8.

$$\frac{3}{2}x-\frac{5}{2}=\frac{8}{5}x+\frac{2}{5}\times 9$$

Express \frac{2}{5}\times 9 as a single fraction.

$$\frac{3}{2}x-\frac{5}{2}=\frac{8}{5}x+\frac{2\times 9}{5}$$

Multiply 2 and 9 to get 18.

$$\frac{3}{2}x-\frac{5}{2}=\frac{8}{5}x+\frac{18}{5}$$

Subtract \frac{8}{5}x from both sides.

$$\frac{3}{2}x-\frac{5}{2}-\frac{8}{5}x=\frac{18}{5}$$

Combine \frac{3}{2}x and -\frac{8}{5}x to get -\frac{1}{10}x.

$$-\frac{1}{10}x-\frac{5}{2}=\frac{18}{5}$$

Add \frac{5}{2} to both sides.

$$-\frac{1}{10}x=\frac{18}{5}+\frac{5}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{18}{5} and \frac{5}{2} to fractions with denominator 10.

$$-\frac{1}{10}x=\frac{36}{10}+\frac{25}{10}$$

Since \frac{36}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$-\frac{1}{10}x=\frac{36+25}{10}$$

Add 36 and 25 to get 61.

$$-\frac{1}{10}x=\frac{61}{10}$$

Multiply both sides by -10, the reciprocal of -\frac{1}{10}.

$$x=\frac{61}{10}\left(-10\right)$$

Express \frac{61}{10}\left(-10\right) as a single fraction.

$$x=\frac{61\left(-10\right)}{10}$$

Multiply 61 and -10 to get -610.

$$x=\frac{-610}{10}$$

Divide -610 by 10 to get -61.

$$x=-61$$