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

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for x

$x=6$

Steps for Solving Linear Equation

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

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

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

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

Multiply $3$ and $3$ to get $9$.

$$\frac{9}{4}x+\frac{3}{4}\times 2-2=2x+1$$

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

$$\frac{9}{4}x+\frac{3\times 2}{4}-2=2x+1$$

Multiply $3$ and $2$ to get $6$.

$$\frac{9}{4}x+\frac{6}{4}-2=2x+1$$

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

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

Convert $2$ to fraction $\frac{4}{2}$.

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

Since $\frac{3}{2}$ and $\frac{4}{2}$ have the same denominator, subtract them by subtracting their numerators.

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

Subtract $4$ from $3$ to get $-1$.

$$\frac{9}{4}x-\frac{1}{2}=2x+1$$

Subtract $2x$ from both sides.

$$\frac{9}{4}x-\frac{1}{2}-2x=1$$

Combine $\frac{9}{4}x$ and $-2x$ to get $\frac{1}{4}x$.

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

Add $\frac{1}{2}$ to both sides.

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

Convert $1$ to fraction $\frac{2}{2}$.

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

Since $\frac{2}{2}$ and $\frac{1}{2}$ have the same denominator, add them by adding their numerators.

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

Add $2$ and $1$ to get $3$.

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

Multiply both sides by $4$, the reciprocal of $\frac{1}{4}$.

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

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

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

Multiply $3$ and $4$ to get $12$.

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

Divide $12$ by $2$ to get $6$.

$$x=6$$