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

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

Solve for x

$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$

Steps for Solving Linear Equation

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

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

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

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

Multiply $2$ and $2$ to get $4$.

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

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

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

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

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

Express $\frac{4}{5}\times 3$ as a single fraction.

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

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

$$\frac{4}{5}x-\frac{2}{5}=\frac{12}{5}x+\frac{4}{5}\left(-5\right)$$

Express $\frac{4}{5}\left(-5\right)$ as a single fraction.

$$\frac{4}{5}x-\frac{2}{5}=\frac{12}{5}x+\frac{4\left(-5\right)}{5}$$

Multiply $4$ and $-5$ to get $-20$.

$$\frac{4}{5}x-\frac{2}{5}=\frac{12}{5}x+\frac{-20}{5}$$

Divide $-20$ by $5$ to get $-4$.

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

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

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

Combine $\frac{4}{5}x$ and $-\frac{12}{5}x$ to get $-\frac{8}{5}x$.

$$-\frac{8}{5}x-\frac{2}{5}=-4$$

Add $\frac{2}{5}$ to both sides.

$$-\frac{8}{5}x=-4+\frac{2}{5}$$

Convert $-4$ to fraction $-\frac{20}{5}$.

$$-\frac{8}{5}x=-\frac{20}{5}+\frac{2}{5}$$

Since $-\frac{20}{5}$ and $\frac{2}{5}$ have the same denominator, add them by adding their numerators.

$$-\frac{8}{5}x=\frac{-20+2}{5}$$

Add $-20$ and $2$ to get $-18$.

$$-\frac{8}{5}x=-\frac{18}{5}$$

Multiply both sides by $-\frac{5}{8}$, the reciprocal of $-\frac{8}{5}$.

$$x=-\frac{18}{5}\left(-\frac{5}{8}\right)$$

Multiply $-\frac{18}{5}$ times $-\frac{5}{8}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-18\left(-5\right)}{5\times 8}$$

Do the multiplications in the fraction $\frac{-18\left(-5\right)}{5\times 8}$.

$$x=\frac{90}{40}$$

Reduce the fraction $\frac{90}{40}$ to lowest terms by extracting and canceling out $10$.

$$x=\frac{9}{4}$$