Solve (3)/(5)(x-4)-(1)/(3)(2x-9)=(1)/(4)(x-1)-2 | 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

$$\frac{ 3 }{ 5 } (x-4)- \frac{ 1 }{ 3 } (2x-9)= \frac{ 1 }{ 4 } (x-1)-2$$

Solve for x

$x=9$

Steps for Solving Linear Equation

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

$$\frac{3}{5}x+\frac{3}{5}\left(-4\right)-\frac{1}{3}\left(2x-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express $\frac{3}{5}\left(-4\right)$ as a single fraction.

$$\frac{3}{5}x+\frac{3\left(-4\right)}{5}-\frac{1}{3}\left(2x-9\right)=\frac{1}{4}\left(x-1\right)-2$$

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

$$\frac{3}{5}x+\frac{-12}{5}-\frac{1}{3}\left(2x-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Fraction $\frac{-12}{5}$ can be rewritten as $-\frac{12}{5}$ by extracting the negative sign.

$$\frac{3}{5}x-\frac{12}{5}-\frac{1}{3}\left(2x-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Use the distributive property to multiply $-\frac{1}{3}$ by $2x-9$.

$$\frac{3}{5}x-\frac{12}{5}-\frac{1}{3}\times 2x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express $-\frac{1}{3}\times 2$ as a single fraction.

$$\frac{3}{5}x-\frac{12}{5}+\frac{-2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$\frac{3}{5}x-\frac{12}{5}-\frac{2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express $-\frac{1}{3}\left(-9\right)$ as a single fraction.

$$\frac{3}{5}x-\frac{12}{5}-\frac{2}{3}x+\frac{-\left(-9\right)}{3}=\frac{1}{4}\left(x-1\right)-2$$

Multiply $-1$ and $-9$ to get $9$.

$$\frac{3}{5}x-\frac{12}{5}-\frac{2}{3}x+\frac{9}{3}=\frac{1}{4}\left(x-1\right)-2$$

Divide $9$ by $3$ to get $3$.

$$\frac{3}{5}x-\frac{12}{5}-\frac{2}{3}x+3=\frac{1}{4}\left(x-1\right)-2$$

Combine $\frac{3}{5}x$ and $-\frac{2}{3}x$ to get $-\frac{1}{15}x$.

$$-\frac{1}{15}x-\frac{12}{5}+3=\frac{1}{4}\left(x-1\right)-2$$

Convert $3$ to fraction $\frac{15}{5}$.

$$-\frac{1}{15}x-\frac{12}{5}+\frac{15}{5}=\frac{1}{4}\left(x-1\right)-2$$

Since $-\frac{12}{5}$ and $\frac{15}{5}$ have the same denominator, add them by adding their numerators.

$$-\frac{1}{15}x+\frac{-12+15}{5}=\frac{1}{4}\left(x-1\right)-2$$

Add $-12$ and $15$ to get $3$.

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}\left(x-1\right)-2$$

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

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}x+\frac{1}{4}\left(-1\right)-2$$

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

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}x-\frac{1}{4}-2$$

Convert $2$ to fraction $\frac{8}{4}$.

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}x-\frac{1}{4}-\frac{8}{4}$$

Since $-\frac{1}{4}$ and $\frac{8}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}x+\frac{-1-8}{4}$$

Subtract $8$ from $-1$ to get $-9$.

$$-\frac{1}{15}x+\frac{3}{5}=\frac{1}{4}x-\frac{9}{4}$$

Subtract $\frac{1}{4}x$ from both sides.

$$-\frac{1}{15}x+\frac{3}{5}-\frac{1}{4}x=-\frac{9}{4}$$

Combine $-\frac{1}{15}x$ and $-\frac{1}{4}x$ to get $-\frac{19}{60}x$.

$$-\frac{19}{60}x+\frac{3}{5}=-\frac{9}{4}$$

Subtract $\frac{3}{5}$ from both sides.

$$-\frac{19}{60}x=-\frac{9}{4}-\frac{3}{5}$$

Least common multiple of $4$ and $5$ is $20$. Convert $-\frac{9}{4}$ and $\frac{3}{5}$ to fractions with denominator $20$.

$$-\frac{19}{60}x=-\frac{45}{20}-\frac{12}{20}$$

Since $-\frac{45}{20}$ and $\frac{12}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{60}x=\frac{-45-12}{20}$$

Subtract $12$ from $-45$ to get $-57$.

$$-\frac{19}{60}x=-\frac{57}{20}$$

Multiply both sides by $-\frac{60}{19}$, the reciprocal of $-\frac{19}{60}$.

$$x=-\frac{57}{20}\left(-\frac{60}{19}\right)$$

Multiply $-\frac{57}{20}$ times $-\frac{60}{19}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-57\left(-60\right)}{20\times 19}$$

Do the multiplications in the fraction $\frac{-57\left(-60\right)}{20\times 19}$.

$$x=\frac{3420}{380}$$

Divide $3420$ by $380$ to get $9$.

$$x=9$$