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

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

Solve for x

$$x = -\frac{54}{5} = -10\frac{4}{5} = -10.8$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{2}{3}x+1=\frac{6}{4}x+10$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Combine \frac{2}{3}x and -\frac{3}{2}x to get -\frac{5}{6}x.

$$-\frac{5}{6}x+1=10$$

Subtract 1 from both sides.

$$-\frac{5}{6}x=10-1$$

Subtract 1 from 10 to get 9.

$$-\frac{5}{6}x=9$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.

$$x=9\left(-\frac{6}{5}\right)$$

Express 9\left(-\frac{6}{5}\right) as a single fraction.

$$x=\frac{9\left(-6\right)}{5}$$

Multiply 9 and -6 to get -54.

$$x=\frac{-54}{5}$$

Fraction \frac{-54}{5} can be rewritten as -\frac{54}{5} by extracting the negative sign.

$$x=-\frac{54}{5}$$