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Solving Equations Solutions

• To solve an equation,    isolate    x (or other variable) on    one side    of the equal sign.

• Whatever you do to one side of an equation, you    must    do on the other side to maintain    equality   .

  • You will do the    opposite    (inverse) operation to isolate the variable. For example:
    • 
If 2 is subtracted from x, you will    add    2 to both sides.
    • 
If 3 is multiplied by x, you will    divide    by 3 (or multiply by $\frac{1}{3}$) on both sides.
    • 
With a fraction, if $\frac{4}{5}$ is multiplied by x, you will divide by $\frac{4}{5}$ which is the same as multiplying by the reciprocal $\underline{ \frac{5}{4} }$.

• Remember to combine any    like terms    before solving.
  • 
Your final answer should have all fractions written in    simplest    form.

  • To check that your answer is correct,    substitute    the value of the variable back into the original equation.

Example 1

Solve.

Check

$$\begin{gathered} \frac{2}{7}\left(–14\right)+6=2 \\ –4+6=2 \\ 2=2 ✓ \end{gathered}$$

Example 2

Solve.

Check

$$\begin{gathered} \frac{8}{5}\left(\left(–\frac{53}{16}\right)+3\right)=–\frac{1}{2} \\ \frac{8}{5}\left(\left(–\frac{53}{16}\right)+\frac{48}{16}\right)=–\frac{1}{2} \\ \frac{8}{5}\left(–\frac{5}{16}\right)=–\frac{1}{2} ✓ \end{gathered}$$