Solve (2)/(3)(3x-5)-(3)/(5)(2x-3)=3 | 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

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

Solve for x

$x = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$

Steps for Solving Linear Equation

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

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

Cancel out $3$ and $3$.

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

Express $\frac{2}{3}\left(-5\right)$ as a single fraction.

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

Multiply $2$ and $-5$ to get $-10$.

$$2x+\frac{-10}{3}-\frac{3}{5}\left(2x-3\right)=3$$

Fraction $\frac{-10}{3}$ can be rewritten as $-\frac{10}{3}$ by extracting the negative sign.

$$2x-\frac{10}{3}-\frac{3}{5}\left(2x-3\right)=3$$

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

$$2x-\frac{10}{3}-\frac{3}{5}\times 2x-\frac{3}{5}\left(-3\right)=3$$

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

$$2x-\frac{10}{3}+\frac{-3\times 2}{5}x-\frac{3}{5}\left(-3\right)=3$$

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

$$2x-\frac{10}{3}+\frac{-6}{5}x-\frac{3}{5}\left(-3\right)=3$$

Fraction $\frac{-6}{5}$ can be rewritten as $-\frac{6}{5}$ by extracting the negative sign.

$$2x-\frac{10}{3}-\frac{6}{5}x-\frac{3}{5}\left(-3\right)=3$$

Express $-\frac{3}{5}\left(-3\right)$ as a single fraction.

$$2x-\frac{10}{3}-\frac{6}{5}x+\frac{-3\left(-3\right)}{5}=3$$

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

$$2x-\frac{10}{3}-\frac{6}{5}x+\frac{9}{5}=3$$

Combine $2x$ and $-\frac{6}{5}x$ to get $\frac{4}{5}x$.

$$\frac{4}{5}x-\frac{10}{3}+\frac{9}{5}=3$$

Least common multiple of $3$ and $5$ is $15$. Convert $-\frac{10}{3}$ and $\frac{9}{5}$ to fractions with denominator $15$.

$$\frac{4}{5}x-\frac{50}{15}+\frac{27}{15}=3$$

Since $-\frac{50}{15}$ and $\frac{27}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{4}{5}x+\frac{-50+27}{15}=3$$

Add $-50$ and $27$ to get $-23$.

$$\frac{4}{5}x-\frac{23}{15}=3$$

Add $\frac{23}{15}$ to both sides.

$$\frac{4}{5}x=3+\frac{23}{15}$$

Convert $3$ to fraction $\frac{45}{15}$.

$$\frac{4}{5}x=\frac{45}{15}+\frac{23}{15}$$

Since $\frac{45}{15}$ and $\frac{23}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{4}{5}x=\frac{45+23}{15}$$

Add $45$ and $23$ to get $68$.

$$\frac{4}{5}x=\frac{68}{15}$$

Multiply both sides by $\frac{5}{4}$, the reciprocal of $\frac{4}{5}$.

$$x=\frac{68}{15}\times \frac{5}{4}$$

Multiply $\frac{68}{15}$ times $\frac{5}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{68\times 5}{15\times 4}$$

Do the multiplications in the fraction $\frac{68\times 5}{15\times 4}$.

$$x=\frac{340}{60}$$

Reduce the fraction $\frac{340}{60}$ to lowest terms by extracting and canceling out $20$.

$$x=\frac{17}{3}$$