What you’ll learn to do: Solve one-step equations using whole numbers
How many seashells did Bobby collect?
During his three-day beach vacation, Bobby is collecting seashells. On the last day of his trip, he picks up [latex]7[/latex] seashells and adds them to his bucket. He counts all his seashells and discovers that he has [latex]23[/latex] in all. Knowing this, how can Bobby determine how many shells he picked up over the first two days of his trip? One way he can figure it out is to write an equation. Read on to learn about properties of equations and develop your skills when solving equations.
Before you get started, take this readiness quiz.
readiness quiz
1)
If you missed this problem, review this example.
Evaluate [latex]x+7[/latex] when
- [latex]x=3[/latex]
- [latex]x=12[/latex]
Show Solution
Solution:
1. To evaluate, substitute [latex]3[/latex] for [latex]x[/latex] in the expression, and then simplify.
|
[latex]x+7[/latex] |
| Substitute. |
[latex]\color{red}{3}+7[/latex] |
| Add. |
[latex]10[/latex] |
When [latex]x=3[/latex], the expression [latex]x+7[/latex] has a value of [latex]10[/latex].
2. To evaluate, substitute [latex]12[/latex] for [latex]x[/latex] in the expression, and then simplify.
|
[latex]x+7[/latex] |
| Substitute. |
[latex]\color{red}{12}+7[/latex] |
| Add. |
[latex]19[/latex] |
When [latex]x=12[/latex], the expression [latex]x+7[/latex] has a value of [latex]19[/latex].
Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.
2)
If you missed this problem, review the example below.
Evaluate [latex]9x - 2,[/latex] when
- [latex]x=5[/latex]
- [latex]x=1[/latex]
Show Solution
Solution
Remember [latex]ab[/latex] means [latex]a[/latex] times [latex]b[/latex], so [latex]9x[/latex] means [latex]9[/latex] times [latex]x[/latex].
1. To evaluate the expression when [latex]x=5[/latex], we substitute [latex]5[/latex] for [latex]x[/latex], and then simplify.
|
[latex]9x-2[/latex] |
| Substitute [latex]\color{red}{5}[/latex] for x. |
[latex]9\cdot\color{red}{5}-2[/latex] |
| Multiply. |
[latex]45-2[/latex] |
| Subtract. |
[latex]43[/latex] |
2. To evaluate the expression when [latex]x=1[/latex], we substitute [latex]1[/latex] for [latex]x[/latex], and then simplify.
|
[latex]9x-2[/latex] |
| Substitute [latex]\color{red}{1}[/latex] for x. |
[latex]9(\color{red}{1})-2[/latex] |
| Multiply. |
[latex]9-2[/latex] |
| Subtract. |
[latex]7[/latex] |
Notice that in part 1 that we wrote [latex]9\cdot 5[/latex] and in part 2 we wrote [latex]9\left(1\right)[/latex]. Both the dot and the parentheses tell us to multiply.
3)
If you missed this problem, review the following video.
When some people hear the word algebra, they think of solving equations. The applications of solving equations are limitless and extend to all careers and fields. In this section, we will begin solving equations. We will start by solving basic equations, and then as we proceed through the course we will build up our skills to cover many different forms of equations.
