Solve (9)/(20)((4)/(3)x-(5)/(6))+(1)/(4)-(3)/(10)x=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

$$\frac{ 9 }{ 20 } ( \frac{ 4 }{ 3 } x- \frac{ 5 }{ 6 } )+ \frac{ 1 }{ 4 } - \frac{ 3 }{ 10 } x=1$$

Solve for x

$x = \frac{15}{4} = 3\frac{3}{4} = 3.75$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{9}{20}$ by $\frac{4}{3}x-\frac{5}{6}$.

$$\frac{9}{20}\times \frac{4}{3}x+\frac{9}{20}\left(-\frac{5}{6}\right)+\frac{1}{4}-\frac{3}{10}x=1$$

Multiply $\frac{9}{20}$ times $\frac{4}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 4}{20\times 3}x+\frac{9}{20}\left(-\frac{5}{6}\right)+\frac{1}{4}-\frac{3}{10}x=1$$

Do the multiplications in the fraction $\frac{9\times 4}{20\times 3}$.

$$\frac{36}{60}x+\frac{9}{20}\left(-\frac{5}{6}\right)+\frac{1}{4}-\frac{3}{10}x=1$$

Reduce the fraction $\frac{36}{60}$ to lowest terms by extracting and canceling out $12$.

$$\frac{3}{5}x+\frac{9}{20}\left(-\frac{5}{6}\right)+\frac{1}{4}-\frac{3}{10}x=1$$

Multiply $\frac{9}{20}$ times $-\frac{5}{6}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}x+\frac{9\left(-5\right)}{20\times 6}+\frac{1}{4}-\frac{3}{10}x=1$$

Do the multiplications in the fraction $\frac{9\left(-5\right)}{20\times 6}$.

$$\frac{3}{5}x+\frac{-45}{120}+\frac{1}{4}-\frac{3}{10}x=1$$

Reduce the fraction $\frac{-45}{120}$ to lowest terms by extracting and canceling out $15$.

$$\frac{3}{5}x-\frac{3}{8}+\frac{1}{4}-\frac{3}{10}x=1$$

Least common multiple of $8$ and $4$ is $8$. Convert $-\frac{3}{8}$ and $\frac{1}{4}$ to fractions with denominator $8$.

$$\frac{3}{5}x-\frac{3}{8}+\frac{2}{8}-\frac{3}{10}x=1$$

Since $-\frac{3}{8}$ and $\frac{2}{8}$ have the same denominator, add them by adding their numerators.

$$\frac{3}{5}x+\frac{-3+2}{8}-\frac{3}{10}x=1$$

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

$$\frac{3}{5}x-\frac{1}{8}-\frac{3}{10}x=1$$

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

$$\frac{3}{10}x-\frac{1}{8}=1$$

Add $\frac{1}{8}$ to both sides.

$$\frac{3}{10}x=1+\frac{1}{8}$$

Convert $1$ to fraction $\frac{8}{8}$.

$$\frac{3}{10}x=\frac{8}{8}+\frac{1}{8}$$

Since $\frac{8}{8}$ and $\frac{1}{8}$ have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x=\frac{8+1}{8}$$

Add $8$ and $1$ to get $9$.

$$\frac{3}{10}x=\frac{9}{8}$$

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

$$x=\frac{9}{8}\times \frac{10}{3}$$

Multiply $\frac{9}{8}$ times $\frac{10}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{9\times 10}{8\times 3}$$

Do the multiplications in the fraction $\frac{9\times 10}{8\times 3}$.

$$x=\frac{90}{24}$$

Reduce the fraction $\frac{90}{24}$ to lowest terms by extracting and canceling out $6$.

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