Solve n : (17(2 - x) - 5(x + 12))/(1 - 7x) = 8 | 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

$$n : \frac { 17 ( 2 - x ) - 5 ( x + 12 ) } { 1 - 7 x } = 8$$

Solve for n

$n=-\frac{16\left(11x+13\right)}{1-7x}$
$x\neq -\frac{13}{11}\text{ and }x\neq \frac{1}{7}$

Steps for Solving Linear Equation

Divide $n$ by $\frac{17\left(2-x\right)-5\left(x+12\right)}{1-7x}$ by multiplying $n$ by the reciprocal of $\frac{17\left(2-x\right)-5\left(x+12\right)}{1-7x}$.

$$\frac{n\left(1-7x\right)}{17\left(2-x\right)-5\left(x+12\right)}=8$$

Use the distributive property to multiply $n$ by $1-7x$.

$$\frac{n-7nx}{17\left(2-x\right)-5\left(x+12\right)}=8$$

Use the distributive property to multiply $17$ by $2-x$.

$$\frac{n-7nx}{34-17x-5\left(x+12\right)}=8$$

Use the distributive property to multiply $-5$ by $x+12$.

$$\frac{n-7nx}{34-17x-5x-60}=8$$

Combine $-17x$ and $-5x$ to get $-22x$.

$$\frac{n-7nx}{34-22x-60}=8$$

Subtract $60$ from $34$ to get $-26$.

$$\frac{n-7nx}{-26-22x}=8$$

Multiply both sides of the equation by $2\left(-11x-13\right)$.

$$n-7nx=16\left(-11x-13\right)$$

Use the distributive property to multiply $16$ by $-11x-13$.

$$n-7nx=-176x-208$$

Combine all terms containing $n$.

$$\left(1-7x\right)n=-176x-208$$

Divide both sides by $1-7x$.

$$\frac{\left(1-7x\right)n}{1-7x}=\frac{-176x-208}{1-7x}$$

Dividing by $1-7x$ undoes the multiplication by $1-7x$.

$$n=\frac{-176x-208}{1-7x}$$

Divide $-176x-208$ by $1-7x$.

$$n=-\frac{16\left(11x+13\right)}{1-7x}$$

Solve for x

$x=-\frac{n+208}{176-7n}$
$n\neq 0\text{ and }n\neq \frac{176}{7}$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $\frac{1}{7}$ since division by zero is not defined. Divide $n$ by $\frac{17\left(2-x\right)-5\left(x+12\right)}{1-7x}$ by multiplying $n$ by the reciprocal of $\frac{17\left(2-x\right)-5\left(x+12\right)}{1-7x}$.

$$\frac{n\left(1-7x\right)}{17\left(2-x\right)-5\left(x+12\right)}=8$$

Use the distributive property to multiply $n$ by $1-7x$.

$$\frac{n-7nx}{17\left(2-x\right)-5\left(x+12\right)}=8$$

Use the distributive property to multiply $17$ by $2-x$.

$$\frac{n-7nx}{34-17x-5\left(x+12\right)}=8$$

Use the distributive property to multiply $-5$ by $x+12$.

$$\frac{n-7nx}{34-17x-5x-60}=8$$

Combine $-17x$ and $-5x$ to get $-22x$.

$$\frac{n-7nx}{34-22x-60}=8$$

Subtract $60$ from $34$ to get $-26$.

$$\frac{n-7nx}{-26-22x}=8$$

Variable $x$ cannot be equal to $-\frac{13}{11}$ since division by zero is not defined. Multiply both sides of the equation by $2\left(-11x-13\right)$.

$$n-7nx=16\left(-11x-13\right)$$

Use the distributive property to multiply $16$ by $-11x-13$.

$$n-7nx=-176x-208$$

Add $176x$ to both sides.

$$n-7nx+176x=-208$$

Subtract $n$ from both sides.

$$-7nx+176x=-208-n$$

Combine all terms containing $x$.

$$\left(-7n+176\right)x=-208-n$$

The equation is in standard form.

$$\left(176-7n\right)x=-n-208$$

Divide both sides by $-7n+176$.

$$\frac{\left(176-7n\right)x}{176-7n}=\frac{-n-208}{176-7n}$$

Dividing by $-7n+176$ undoes the multiplication by $-7n+176$.

$$x=\frac{-n-208}{176-7n}$$

Divide $-208-n$ by $-7n+176$.

$$x=-\frac{n+208}{176-7n}$$

Variable $x$ cannot be equal to any of the values $-\frac{13}{11},\frac{1}{7}$.

$$x=-\frac{n+208}{176-7n}\text{, }x\neq -\frac{13}{11}\text{ and }x\neq \frac{1}{7}$$