Solve 3/4 * (2x - 1) = 2/5 * (3x - 1) - 5 | 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

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

Solve for x

$x = -\frac{31}{2} = -15\frac{1}{2} = -15.5$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{3}{4}$ by $2x-1$.

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

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

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

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

$$\frac{6}{4}x+\frac{3}{4}\left(-1\right)=\frac{2}{5}\left(3x-1\right)-5$$

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

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

Multiply $\frac{3}{4}$ and $-1$ to get $-\frac{3}{4}$.

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

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

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

Express $\frac{2}{5}\times 3$ as a single fraction.

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

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

$$\frac{3}{2}x-\frac{3}{4}=\frac{6}{5}x+\frac{2}{5}\left(-1\right)-5$$

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

$$\frac{3}{2}x-\frac{3}{4}=\frac{6}{5}x-\frac{2}{5}-5$$

Convert $5$ to fraction $\frac{25}{5}$.

$$\frac{3}{2}x-\frac{3}{4}=\frac{6}{5}x-\frac{2}{5}-\frac{25}{5}$$

Since $-\frac{2}{5}$ and $\frac{25}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}x-\frac{3}{4}=\frac{6}{5}x+\frac{-2-25}{5}$$

Subtract $25$ from $-2$ to get $-27$.

$$\frac{3}{2}x-\frac{3}{4}=\frac{6}{5}x-\frac{27}{5}$$

Subtract $\frac{6}{5}x$ from both sides.

$$\frac{3}{2}x-\frac{3}{4}-\frac{6}{5}x=-\frac{27}{5}$$

Combine $\frac{3}{2}x$ and $-\frac{6}{5}x$ to get $\frac{3}{10}x$.

$$\frac{3}{10}x-\frac{3}{4}=-\frac{27}{5}$$

Add $\frac{3}{4}$ to both sides.

$$\frac{3}{10}x=-\frac{27}{5}+\frac{3}{4}$$

Least common multiple of $5$ and $4$ is $20$. Convert $-\frac{27}{5}$ and $\frac{3}{4}$ to fractions with denominator $20$.

$$\frac{3}{10}x=-\frac{108}{20}+\frac{15}{20}$$

Since $-\frac{108}{20}$ and $\frac{15}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x=\frac{-108+15}{20}$$

Add $-108$ and $15$ to get $-93$.

$$\frac{3}{10}x=-\frac{93}{20}$$

Multiply both sides by $\frac{10}{3}$, the reciprocal of $\frac{3}{10}$.

$$x=-\frac{93}{20}\times \frac{10}{3}$$

Multiply $-\frac{93}{20}$ times $\frac{10}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-93\times 10}{20\times 3}$$

Do the multiplications in the fraction $\frac{-93\times 10}{20\times 3}$.

$$x=\frac{-930}{60}$$

Reduce the fraction $\frac{-930}{60}$ to lowest terms by extracting and canceling out $30$.

$$x=-\frac{31}{2}$$