Solve (9x+7)/(2)-(x-(x-2)/(7))=36 | 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

$$\frac{ 9x+7 }{ 2 } -(x- \frac{ x-2 }{ 7 } )=36$$

Solve for x

$x=9$

Steps for Solving Linear Equation

Multiply both sides of the equation by $14$, the least common multiple of $2,7$.

$$7\left(9x+7\right)-14\left(x-\frac{x-2}{7}\right)=504$$

Use the distributive property to multiply $7$ by $9x+7$.

$$63x+49-14\left(x-\frac{x-2}{7}\right)=504$$

Divide each term of $x-2$ by $7$ to get $\frac{1}{7}x-\frac{2}{7}$.

$$63x+49-14\left(x-\left(\frac{1}{7}x-\frac{2}{7}\right)\right)=504$$

To find the opposite of $\frac{1}{7}x-\frac{2}{7}$, find the opposite of each term.

$$63x+49-14\left(x-\frac{1}{7}x-\left(-\frac{2}{7}\right)\right)=504$$

The opposite of $-\frac{2}{7}$ is $\frac{2}{7}$.

$$63x+49-14\left(x-\frac{1}{7}x+\frac{2}{7}\right)=504$$

Combine $x$ and $-\frac{1}{7}x$ to get $\frac{6}{7}x$.

$$63x+49-14\left(\frac{6}{7}x+\frac{2}{7}\right)=504$$

Use the distributive property to multiply $-14$ by $\frac{6}{7}x+\frac{2}{7}$.

$$63x+49-14\times \frac{6}{7}x-14\times \frac{2}{7}=504$$

Express $-14\times \frac{6}{7}$ as a single fraction.

$$63x+49+\frac{-14\times 6}{7}x-14\times \frac{2}{7}=504$$

Multiply $-14$ and $6$ to get $-84$.

$$63x+49+\frac{-84}{7}x-14\times \frac{2}{7}=504$$

Divide $-84$ by $7$ to get $-12$.

$$63x+49-12x-14\times \frac{2}{7}=504$$

Express $-14\times \frac{2}{7}$ as a single fraction.

$$63x+49-12x+\frac{-14\times 2}{7}=504$$

Multiply $-14$ and $2$ to get $-28$.

$$63x+49-12x+\frac{-28}{7}=504$$

Divide $-28$ by $7$ to get $-4$.

$$63x+49-12x-4=504$$

Combine $63x$ and $-12x$ to get $51x$.

$$51x+49-4=504$$

Subtract $4$ from $49$ to get $45$.

$$51x+45=504$$

Subtract $45$ from both sides.

$$51x=504-45$$

Subtract $45$ from $504$ to get $459$.

$$51x=459$$

Divide both sides by $51$.

$$x=\frac{459}{51}$$

Divide $459$ by $51$ to get $9$.

$$x=9$$