3.2: OneStep Equations Transformed by MultiplicationDivision
What if you had an algebraic equation involving multiplication or division like \begin{align*}5x = 3\end{align*}
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CK12 Foundation: 0302S Solving Equations with Multiplication and Division (H264)
Guidance
Suppose you are selling pizza for $1.50 a slice and you can get eight slices out of a single pizza. How much money do you get for a single pizza? It shouldn’t take you long to figure out that you get \begin{align*}8 \times \$1.50 = \$12.00\end{align*}
Example A
Solve \begin{align*} \frac{1}{8} \cdot x = 1.5\end{align*}
Our \begin{align*}x\end{align*}
\begin{align*}8 \left ( \frac{1}{8} \cdot x \right ) &= 8(1.5)\\
x &= 12\end{align*}
Example B
Solve \begin{align*}0.25x = 5.25\end{align*}
0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4.
\begin{align*}4(0.25x) &= 4(5.25)\\
x &= 21\end{align*}
Solving by division is another way to isolate \begin{align*}x\end{align*}
Example C
Solve \begin{align*}5x = 3.25\end{align*}
To cancel the 5, we divide both sides by 5.
\begin{align*} \frac{5x}{5} &= \frac{3.25}{5}\\
x &= 0.65\end{align*}
Example D
Solve \begin{align*}1.375x = 1.2\end{align*}
Divide by 1.375
\begin{align*} x &= \frac{1.2}{1.375}\\
x &= 0.8 \overline{72}\end{align*}
Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272....
To see more examples of one  and twostep equation solving, watch the Khan Academy video series starting at http://www.youtube.com/watch?v=bAerID24QJ0.
Watch this video for help with the Examples above.
CK12 Foundation: Solving Equations with Multiplication and Division
Vocabulary
 An equation in which each term is either a constant or the product of a constant and a single variable is a linear equation.
 We can add, subtract, multiply, or divide both sides of an equation by the same value and still have an equivalent equation.
 To solve an equation, isolate the unknown variable on one side of the equation by applying one or more arithmetic operations to both sides.
Guided Practice
Solve:
a) \begin{align*} \frac{9x}{5} = 5\end{align*}
b) \begin{align*}7x = \frac{5}{11}\end{align*}
Solutions:
a) \begin{align*}\frac{9x}{5}\end{align*}
\begin{align*} \frac{5}{9} \left ( \frac{9x}{5} \right ) &= \frac{5}{9}(5)\\
x &= \frac{25}{9}\end{align*}
b) Divide both sides by 7.
\begin{align*}x &= \frac{5}{11.7}\\
x &= \frac{5}{77} \end{align*}
Practice
For 15, solve the following equations for \begin{align*}x\end{align*}

\begin{align*}7x = 21 \end{align*}
7x=21 
\begin{align*}4x = 1 \end{align*}
4x=1 
\begin{align*}\frac{5x}{12} = \frac{2}{3}\end{align*}
5x12=23 
\begin{align*}0.01x = 11\end{align*}
0.01x=11 
\begin{align*}\frac{2x}{9} = \frac{10}{3}\end{align*}
−2x9=103
For 610, solve the following equations for the unknown variable.

\begin{align*}21s = 3 \end{align*}
21s=3 
\begin{align*}7a = 5 \end{align*}
−7a=−5 
\begin{align*}\frac{7f}{11} = \frac{7}{11} \end{align*}
7f11=711 
\begin{align*}6r = \frac{3}{8} \end{align*}
6r=38 
\begin{align*}\frac{9b}{16} = \frac{3}{8} \end{align*}
9b16=38
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Here you'll learn how to use multiplication and division to solve algebraic equations for their unknown variable.