Solve e equation : (9p + 7)/2 - (1 + p - (p - 2)/7) = 35 | 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

$$\frac { 9 p + 7 } { 2 } - ( 1 + p - \frac { p - 2 } { 7 } ) = 35$$

Solve for p

$p=9$

Steps for Solving Linear Equation

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

$$7\left(9p+7\right)-14\left(1+p-\frac{p-2}{7}\right)=490$$

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

$$63p+49-14\left(1+p-\frac{p-2}{7}\right)=490$$

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

$$63p+49-14\left(1+p-\left(\frac{1}{7}p-\frac{2}{7}\right)\right)=490$$

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

$$63p+49-14\left(1+p-\frac{1}{7}p-\left(-\frac{2}{7}\right)\right)=490$$

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

$$63p+49-14\left(1+p-\frac{1}{7}p+\frac{2}{7}\right)=490$$

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

$$63p+49-14\left(1+\frac{6}{7}p+\frac{2}{7}\right)=490$$

Convert $1$ to fraction $\frac{7}{7}$.

$$63p+49-14\left(\frac{7}{7}+\frac{6}{7}p+\frac{2}{7}\right)=490$$

Since $\frac{7}{7}$ and $\frac{2}{7}$ have the same denominator, add them by adding their numerators.

$$63p+49-14\left(\frac{7+2}{7}+\frac{6}{7}p\right)=490$$

Add $7$ and $2$ to get $9$.

$$63p+49-14\left(\frac{9}{7}+\frac{6}{7}p\right)=490$$

Use the distributive property to multiply $-14$ by $\frac{9}{7}+\frac{6}{7}p$.

$$63p+49-14\times \frac{9}{7}-14\times \frac{6}{7}p=490$$

Express $-14\times \frac{9}{7}$ as a single fraction.

$$63p+49+\frac{-14\times 9}{7}-14\times \frac{6}{7}p=490$$

Multiply $-14$ and $9$ to get $-126$.

$$63p+49+\frac{-126}{7}-14\times \frac{6}{7}p=490$$

Divide $-126$ by $7$ to get $-18$.

$$63p+49-18-14\times \frac{6}{7}p=490$$

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

$$63p+49-18+\frac{-14\times 6}{7}p=490$$

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

$$63p+49-18+\frac{-84}{7}p=490$$

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

$$63p+49-18-12p=490$$

Subtract $18$ from $49$ to get $31$.

$$63p+31-12p=490$$

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

$$51p+31=490$$

Subtract $31$ from both sides.

$$51p=490-31$$

Subtract $31$ from $490$ to get $459$.

$$51p=459$$

Divide both sides by $51$.

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

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

$$p=9$$