To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality.

14 = - 2 k + 3

$LHS - 3 = RHS - 3$

14 - 3 = - 2 k + 3 - 3

Subtract terms

11 = - 2 k

Rearrange equation

- 2 k = 11

Now we can continue to solve using the Properties of Equality.

- 2 k = 11

$LHS / - 2 = RHS / - 2$

\frac{- 2 k}{- 2} = \frac{1 1}{- 2}

$\frac{- a}{- b} = \frac{a}{b}$

\frac{2 k}{2} = \frac{1 1}{- 2}

Put minus sign in front of fraction

\frac{2 k}{2} = - \frac{1 1}{2}

Calculate quotient

k = - \frac{1 1}{2}

The solution to the equation is

k = - \frac{1 1}{2} .

We can check our solution by substituting it into the original equation.

14 = - 2 k + 3

$k = - \frac{1 1}{2}$

14 = ? - 2 (- \frac{1 1}{2}) + 3

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Simplify

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

14 = ? - \frac{- 2 ( 1 1 )}{2} + 3

14 = ? - \frac{- 2 2}{2} + 3

Put minus sign in front of fraction

14 = ? - (- \frac{2 2}{2}) + 3

$- (- a) = a$

14 = ? \frac{2 2}{2} + 3

Calculate quotient

14 = ? 11 + 3

Add terms

14 = 14

Since the left-hand side is equal to the right-hand side, our solution is correct.

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