Solve 3(n - 4) + 2(4n - 5) = 5(n + 2) + 16 | 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

$$3(n-4)+2(4n-5)=5(n+2)+16$$

Solve for n

$n=8$

Steps for Solving Linear Equation

Use the distributive property to multiply $3$ by $n-4$.

$$3n-12+2\left(4n-5\right)=5\left(n+2\right)+16$$

Use the distributive property to multiply $2$ by $4n-5$.

$$3n-12+8n-10=5\left(n+2\right)+16$$

Combine $3n$ and $8n$ to get $11n$.

$$11n-12-10=5\left(n+2\right)+16$$

Subtract $10$ from $-12$ to get $-22$.

$$11n-22=5\left(n+2\right)+16$$

Use the distributive property to multiply $5$ by $n+2$.

$$11n-22=5n+10+16$$

Add $10$ and $16$ to get $26$.

$$11n-22=5n+26$$

Subtract $5n$ from both sides.

$$11n-22-5n=26$$

Combine $11n$ and $-5n$ to get $6n$.

$$6n-22=26$$

Add $22$ to both sides.

$$6n=26+22$$

Add $26$ and $22$ to get $48$.

$$6n=48$$

Divide both sides by $6$.

$$n=\frac{48}{6}$$

Divide $48$ by $6$ to get $8$.

$$n=8$$