Solve (3(X-3))/(x+20)=(1)/(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

$$\frac{ 3(X-3) }{ x+20 } = \frac{ 1 }{ 8 }$$

Solve for X

$X=\frac{x+92}{24}$
$x\neq -20$

Steps for Solving Linear Equation

Multiply both sides of the equation by $8\left(x+20\right)$, the least common multiple of $x+20,8$.

$$8\times 3\left(X-3\right)=x+20$$

Multiply $8$ and $3$ to get $24$.

$$24\left(X-3\right)=x+20$$

Use the distributive property to multiply $24$ by $X-3$.

$$24X-72=x+20$$

Add $72$ to both sides.

$$24X=x+20+72$$

Add $20$ and $72$ to get $92$.

$$24X=x+92$$

Divide both sides by $24$.

$$\frac{24X}{24}=\frac{x+92}{24}$$

Dividing by $24$ undoes the multiplication by $24$.

$$X=\frac{x+92}{24}$$

Divide $x+92$ by $24$.

$$X=\frac{x}{24}+\frac{23}{6}$$

Solve for x

$x=24X-92$
$X\neq 3$

Solution Steps

Variable $x$ cannot be equal to $-20$ since division by zero is not defined. Multiply both sides of the equation by $8\left(x+20\right)$, the least common multiple of $x+20,8$.

$$8\times 3\left(X-3\right)=x+20$$

Multiply $8$ and $3$ to get $24$.

$$24\left(X-3\right)=x+20$$

Use the distributive property to multiply $24$ by $X-3$.

$$24X-72=x+20$$

Swap sides so that all variable terms are on the left hand side.

$$x+20=24X-72$$

Subtract $20$ from both sides.

$$x=24X-72-20$$

Subtract $20$ from $-72$ to get $-92$.

$$x=24X-92$$

Variable $x$ cannot be equal to $-20$.

$$x=24X-92\text{, }x\neq -20$$