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# One-Step Equations Transformed by Multiplication/Division

Multiplication or division to solve an equation.
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Practice One-Step Equations Transformed by Multiplication/Division
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One-Step Equations Transformed by Multiplication/Division

What if you had an algebraic equation involving multiplication or division like $-5x = 3$ ? How could you solve it for the unknown variable x ? After completing this Concept, you'll be able to solve equations like this one.

### Guidance

#### Example C

Solve $5x = 3.25$ .

To cancel the 5, we divide both sides by 5.

$\frac{5x}{5} &= \frac{3.25}{5}\\x &= 0.65$

#### Example D

Solve $1.375x = 1.2$ .

Divide by 1.375

$x &= \frac{1.2}{1.375}\\x &= 0.8 \overline{72}$

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 two-step 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.

### 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) $\frac{9x}{5} = 5$ .

b) $7x = \frac{5}{11}$ .

Solutions:

a) $\frac{9x}{5}$ is equivalent to $\frac{9}{5} \cdot x$ , so to cancel out that $\frac{9}{5}$ , we multiply by the reciprocal, $\frac{5}{9}$ .

$\frac{5}{9} \left ( \frac{9x}{5} \right ) &= \frac{5}{9}(5)\\x &= \frac{25}{9}$

b) Divide both sides by 7.

$x &= \frac{5}{11.7}\\x &= \frac{5}{77}$

### Practice

For 1-5, solve the following equations for $x$ .

1. $7x = 21$
2. $4x = 1$
3. $\frac{5x}{12} = \frac{2}{3}$
4. $0.01x = 11$
5. $\frac{-2x}{9} = \frac{10}{3}$

For 6-10, solve the following equations for the unknown variable.

1. $21s = 3$
2. $-7a = -5$
3. $\frac{7f}{11} = \frac{7}{11}$
4. $6r = \frac{3}{8}$
5. $\frac{9b}{16} = \frac{3}{8}$