# One-Step Equations Containing Decimals

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After defining one–step equations and learning how to solve those if they contained integers, now let us learn how to solve one–step equations containing decimals. The rules for solving one–step equations containing integers still hold true for one–step equations involving decimals. Likewise, the underlying objective is to separate the variable and the constant part, by placing the variable on the left side and the constant on the right side of the equation. This can be done by doing the opposite of whatever operation is involved in the original equation or by performing the inverse of what is being done to the variable. Since decimals are involved, please note the rules for performing operations with decimals.

Listed below are some examples of one–step equations containing decimals:

1. $a+0.2=1.5$
2. $b-2.3=3.4$
3. $w+0.25=6.75$
4. $z-1.725=0.002$
5. $3w=2.4$
6. $0.03a=24.6$
7. $\displaystyle \frac{h}{0.5}=2.1$

## Solving One – step Equations Containing Decimals

To solve one–step equation, do the inverse of the operation involved. Since, we are dealing with equations, it must be noted that whatever operation is done on one side of the equation must as well be done on the other side of the equation. Also, apply the rules for performing operations with decimals. To illustrate, consider the following examples:

Solve for the unknown variable:

1. $a+0.2=1.5$

Solution:

To solve for $a$, we subtract 0.2 to both sides of the equation.

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &a+0.2&=&1.5 \\ &a+0.2-0.2&=&1.5-0.2 \\ &\therefore a&=&1.3 \\ \end{array}$

2. $b-2.3=3.4$

Solution:

To solve for $b$, add 2.3 to both sides then simplify the decimals on the right side of the equation.

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &b-2.3&=&3.4 \\ &b-2.3+2.3&=&3.4+2.3 \\ &\therefore b&=&5.7 \\ \end{array}$

3. $3w=2.4$

Solution:

To solve for $w$, divide both sides by 3, then simplify the constant part.

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &3w&=&2.4 \\ &\displaystyle \frac{3w}{3}&=&\displaystyle \frac{2.4}{3} \\ &\therefore w&=&0.8 \\ \end{array}$

4. $\displaystyle \frac{h}{0.5}=2.1$

Solution:

To solve for $h$, multiply both sides by 0.05 then simplify the constant part.

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &\displaystyle \frac{h}{0.5}&=&2.1 \\ &\left (0.5 \right )\displaystyle \frac{h}{0.5}&=&2.1\left ( 0.5 \right ) \\ &\therefore h&=&1.05 \\ \end{array}$

Practice Exercises

Solve for the unknown variable.

1. $a-0.12=1.2$
2. $b+1.3=2.3$
3. $2c=12.4$
4. $0.2d=26.8$
5. $\displaystyle \frac{e}{1.2}=14.4$