What you’ll learn to do: Solve one-step equations using integers
The apples are picked–now it’s time to divvy them up!
After a day of apple picking, Jessica, Mark, and Kim decide to split up their apples equally. In their shared basket, they count [latex]39[/latex] apples total. How many apples can each of them take home? To find out, they’ll need to use division in a one-step variable equation. In this section, you’ll learn how to maintain equality on both sides of the equation and solve for a variable.
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].
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
