Solve 5y-1/3+2/9=2/3-1/9-3/9 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

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a⋅(b-2)=3b

Question

$$5y-1/3+2/9=2/3-1/9-3/9$$

Solve for y

$y=\frac{1}{15}\approx 0.066666667$

Steps for Solving Linear Equation

Least common multiple of $3$ and $9$ is $9$. Convert $-\frac{1}{3}$ and $\frac{2}{9}$ to fractions with denominator $9$.

$$5y-\frac{3}{9}+\frac{2}{9}=\frac{2}{3}-\frac{1}{9}-\frac{3}{9}$$

Since $-\frac{3}{9}$ and $\frac{2}{9}$ have the same denominator, add them by adding their numerators.

$$5y+\frac{-3+2}{9}=\frac{2}{3}-\frac{1}{9}-\frac{3}{9}$$

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

$$5y-\frac{1}{9}=\frac{2}{3}-\frac{1}{9}-\frac{3}{9}$$

Least common multiple of $3$ and $9$ is $9$. Convert $\frac{2}{3}$ and $\frac{1}{9}$ to fractions with denominator $9$.

$$5y-\frac{1}{9}=\frac{6}{9}-\frac{1}{9}-\frac{3}{9}$$

Since $\frac{6}{9}$ and $\frac{1}{9}$ have the same denominator, subtract them by subtracting their numerators.

$$5y-\frac{1}{9}=\frac{6-1}{9}-\frac{3}{9}$$

Subtract $1$ from $6$ to get $5$.

$$5y-\frac{1}{9}=\frac{5}{9}-\frac{3}{9}$$

Reduce the fraction $\frac{3}{9}$ to lowest terms by extracting and canceling out $3$.

$$5y-\frac{1}{9}=\frac{5}{9}-\frac{1}{3}$$

Least common multiple of $9$ and $3$ is $9$. Convert $\frac{5}{9}$ and $\frac{1}{3}$ to fractions with denominator $9$.

$$5y-\frac{1}{9}=\frac{5}{9}-\frac{3}{9}$$

Since $\frac{5}{9}$ and $\frac{3}{9}$ have the same denominator, subtract them by subtracting their numerators.

$$5y-\frac{1}{9}=\frac{5-3}{9}$$

Subtract $3$ from $5$ to get $2$.

$$5y-\frac{1}{9}=\frac{2}{9}$$

Add $\frac{1}{9}$ to both sides.

$$5y=\frac{2}{9}+\frac{1}{9}$$

Since $\frac{2}{9}$ and $\frac{1}{9}$ have the same denominator, add them by adding their numerators.

$$5y=\frac{2+1}{9}$$

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

$$5y=\frac{3}{9}$$

Reduce the fraction $\frac{3}{9}$ to lowest terms by extracting and canceling out $3$.

$$5y=\frac{1}{3}$$

Divide both sides by $5$.

$$y=\frac{\frac{1}{3}}{5}$$

Express $\frac{\frac{1}{3}}{5}$ as a single fraction.

$$y=\frac{1}{3\times 5}$$

Multiply $3$ and $5$ to get $15$.

$$y=\frac{1}{15}$$