Solve x/2 - (3n)/4 + (5n)/6 = 21 | 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

$$\frac{x}{2}-\frac{3n}{4}+\frac{5n}{6}=21$$

Solve for n

$n=252-6x$

Solution Steps

Multiply both sides of the equation by $12$, the least common multiple of $2,4,6$.

$$6x-3\times 3n+2\times 5n=252$$

Multiply $-3$ and $3$ to get $-9$.

$$6x-9n+2\times 5n=252$$

Multiply $2$ and $5$ to get $10$.

$$6x-9n+10n=252$$

Combine $-9n$ and $10n$ to get $n$.

$$6x+n=252$$

Subtract $6x$ from both sides.

$$n=252-6x$$

Solve for x

$x=-\frac{n}{6}+42$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $2,4,6$.

$$6x-3\times 3n+2\times 5n=252$$

Multiply $-3$ and $3$ to get $-9$.

$$6x-9n+2\times 5n=252$$

Multiply $2$ and $5$ to get $10$.

$$6x-9n+10n=252$$

Combine $-9n$ and $10n$ to get $n$.

$$6x+n=252$$

Subtract $n$ from both sides.

$$6x=252-n$$

Divide both sides by $6$.

$$\frac{6x}{6}=\frac{252-n}{6}$$

Dividing by $6$ undoes the multiplication by $6$.

$$x=\frac{252-n}{6}$$

Divide $252-n$ by $6$.

$$x=-\frac{n}{6}+42$$