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

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

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

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

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

Subtract 2x from both sides.

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

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

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

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

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

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

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

Since -\frac{3}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from -3 to get -7.

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

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

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

Multiply -\frac{7}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-7\left(-3\right)}{3\times 2}.

$$x=\frac{21}{6}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{7}{2}$$