Solve (5n)/3 + 9/5 = (7n)/5 + 3/10 | 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

$$\frac{5n}{3}+\frac{9}{5}=\frac{7n}{5}+\frac{3}{10}$$

Solve for n

$n = -\frac{45}{8} = -5\frac{5}{8} = -5.625$

Steps for Solving Linear Equation

Multiply both sides of the equation by $30$, the least common multiple of $3,5,10$.

$$10\times 5n+54=6\times 7n+9$$

Multiply $10$ and $5$ to get $50$.

$$50n+54=6\times 7n+9$$

Multiply $6$ and $7$ to get $42$.

$$50n+54=42n+9$$

Subtract $42n$ from both sides.

$$50n+54-42n=9$$

Combine $50n$ and $-42n$ to get $8n$.

$$8n+54=9$$

Subtract $54$ from both sides.

$$8n=9-54$$

Subtract $54$ from $9$ to get $-45$.

$$8n=-45$$

Divide both sides by $8$.

$$n=\frac{-45}{8}$$

Fraction $\frac{-45}{8}$ can be rewritten as $-\frac{45}{8}$ by extracting the negative sign.

$$n=-\frac{45}{8}$$