Question

solve the following linear equations.
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Answer 1

Linear Equation

1. $\frac{x}{2} - \frac{1}{5} = \frac{x}{3} +\frac{1}{4}$

Step 1: Simplify both sides of the equation.

$\frac{1}{2} x +\frac{-1}{5} = \frac{1}{3} x+\frac{1}{4}$

Step 2: Subtract  $\frac{1}{3} x$  from both sides.

$\frac{1}{2} x +\frac{-1}{5}-\frac{1}{3} x = \frac{1}{3} x +\frac{1}{4} -\frac{1}{3} x$

$\frac{1}{6}x+\frac{-1}{5} =\frac{1}{4}$

Step 3: Add  $\frac{1}{5}$  to both sides.

$\frac{1}{6} x+\frac{-1}{5} +\frac{1}{5} = \frac{1}{4} + \frac{1}{5}$

$\frac{1}{6} x = \frac{9}{20}$

Step 4: Multiply both sides by 6.

$6*\frac{1}{6} x = 6*\frac{9}{20}$

∴ $x = \frac{27}{10}$

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

Step 1: Simplify both sides of the equation.

$\frac{1}{2} n + \frac{-3}{4} n +\frac{5}{6} n = 21$

Combine Like terms ⇒

$(\frac{1}{2} n + \frac{-3}{4} n +\frac{5}{6} n )= 21$

$\frac{7}{12} n = 21$

Step 2: Multiply both sides by $\frac{12}{7}$.

$\frac{12}{7} * (\frac{7}{12} n) = \frac{12}{7} *21$

∴ $n = 36$