Solve (5(3-(5)/(12)))/(4)+((35)/(12)+8)/(6)=3((5)/(12)+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

$$\frac{ 5(3- \frac{ 5 }{ 12 } ) }{ 4 } + \frac{ \frac{ 35 }{ 12 } +8 }{ 6 } =3( \frac{ 5 }{ 12 } +1)$$

Verify

$\text{false}$

Solution Steps

Multiply both sides of the equation by $12$, the least common multiple of $4,6,12$.

$$3\times 5\left(3-\frac{5}{12}\right)+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

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

$$15\left(3-\frac{5}{12}\right)+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Convert $3$ to fraction $\frac{36}{12}$.

$$15\left(\frac{36}{12}-\frac{5}{12}\right)+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Since $\frac{36}{12}$ and $\frac{5}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$15\times \frac{36-5}{12}+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Subtract $5$ from $36$ to get $31$.

$$15\times \frac{31}{12}+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Express $15\times \frac{31}{12}$ as a single fraction.

$$\frac{15\times 31}{12}+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Multiply $15$ and $31$ to get $465$.

$$\frac{465}{12}+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Reduce the fraction $\frac{465}{12}$ to lowest terms by extracting and canceling out $3$.

$$\frac{155}{4}+2\left(\frac{35}{12}+8\right)=36\left(\frac{5}{12}+1\right)$$

Convert $8$ to fraction $\frac{96}{12}$.

$$\frac{155}{4}+2\left(\frac{35}{12}+\frac{96}{12}\right)=36\left(\frac{5}{12}+1\right)$$

Since $\frac{35}{12}$ and $\frac{96}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{155}{4}+2\times \frac{35+96}{12}=36\left(\frac{5}{12}+1\right)$$

Add $35$ and $96$ to get $131$.

$$\frac{155}{4}+2\times \frac{131}{12}=36\left(\frac{5}{12}+1\right)$$

Express $2\times \frac{131}{12}$ as a single fraction.

$$\frac{155}{4}+\frac{2\times 131}{12}=36\left(\frac{5}{12}+1\right)$$

Multiply $2$ and $131$ to get $262$.

$$\frac{155}{4}+\frac{262}{12}=36\left(\frac{5}{12}+1\right)$$

Reduce the fraction $\frac{262}{12}$ to lowest terms by extracting and canceling out $2$.

$$\frac{155}{4}+\frac{131}{6}=36\left(\frac{5}{12}+1\right)$$

Least common multiple of $4$ and $6$ is $12$. Convert $\frac{155}{4}$ and $\frac{131}{6}$ to fractions with denominator $12$.

$$\frac{465}{12}+\frac{262}{12}=36\left(\frac{5}{12}+1\right)$$

Since $\frac{465}{12}$ and $\frac{262}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{465+262}{12}=36\left(\frac{5}{12}+1\right)$$

Add $465$ and $262$ to get $727$.

$$\frac{727}{12}=36\left(\frac{5}{12}+1\right)$$

Convert $1$ to fraction $\frac{12}{12}$.

$$\frac{727}{12}=36\left(\frac{5}{12}+\frac{12}{12}\right)$$

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

$$\frac{727}{12}=36\times \frac{5+12}{12}$$

Add $5$ and $12$ to get $17$.

$$\frac{727}{12}=36\times \frac{17}{12}$$

Express $36\times \frac{17}{12}$ as a single fraction.

$$\frac{727}{12}=\frac{36\times 17}{12}$$

Multiply $36$ and $17$ to get $612$.

$$\frac{727}{12}=\frac{612}{12}$$

Compare $\frac{727}{12}$ and $\frac{612}{12}$.

$$\text{false}$$