How to solve 3/4=2/3(x+1)-1/4

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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

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Question

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

Solve for x

$x=\frac{1}{2}=0.5$

Steps for Solving Linear Equation

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

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

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{2}{3}$ and $\frac{1}{4}$ to fractions with denominator $12$.

$$\frac{3}{4}=\frac{2}{3}x+\frac{8}{12}-\frac{3}{12}$$

Since $\frac{8}{12}$ and $\frac{3}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}=\frac{2}{3}x+\frac{8-3}{12}$$

Subtract $3$ from $8$ to get $5$.

$$\frac{3}{4}=\frac{2}{3}x+\frac{5}{12}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2}{3}x+\frac{5}{12}=\frac{3}{4}$$

Subtract $\frac{5}{12}$ from both sides.

$$\frac{2}{3}x=\frac{3}{4}-\frac{5}{12}$$

Least common multiple of $4$ and $12$ is $12$. Convert $\frac{3}{4}$ and $\frac{5}{12}$ to fractions with denominator $12$.

$$\frac{2}{3}x=\frac{9}{12}-\frac{5}{12}$$

Since $\frac{9}{12}$ and $\frac{5}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x=\frac{9-5}{12}$$

Subtract $5$ from $9$ to get $4$.

$$\frac{2}{3}x=\frac{4}{12}$$

Reduce the fraction $\frac{4}{12}$ to lowest terms by extracting and canceling out $4$.

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

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

$$x=\frac{1}{3}\times \frac{3}{2}$$

Multiply $\frac{1}{3}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 3}{3\times 2}$$

Cancel out $3$ in both numerator and denominator.

$$x=\frac{1}{2}$$

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