Introduction to Solving One-step Equations Using Integers

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 $39$ 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

If you missed this problem, review this example.

Evaluate $x+7$ when

$x=3$
$x=12$

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Solution:

1. To evaluate, substitute $3$ for $x$ in the expression, and then simplify.

	$x+7$
Substitute.	$\color{red}{3}+7$
Add.	$10$

When $x=3$ , the expression $x+7$ has a value of $10$ .
2. To evaluate, substitute $12$ for $x$ in the expression, and then simplify.

	$x+7$
Substitute.	$\color{red}{12}+7$
Add.	$19$

When $x=12$ , the expression $x+7$ has a value of $19$ .

If you missed this problem, review the example below.

Evaluate $9x - 2,$ when

$x=5$
$x=1$

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Solution
Remember $ab$ means $a$ times $b$ , so $9x$ means $9$ times $x$ .
1. To evaluate the expression when $x=5$ , we substitute $5$ for $x$ , and then simplify.

	$9x-2$
Substitute $\color{red}{5}$ for x.	$9\cdot\color{red}{5}-2$
Multiply.	$45-2$
Subtract.	$43$

2. To evaluate the expression when $x=1$ , we substitute $1$ for $x$ , and then simplify.

	$9x-2$
Substitute $\color{red}{1}$ for x.	$9(\color{red}{1})-2$
Multiply.	$9-2$
Subtract.	$7$

Notice that in part 1 that we wrote $9\cdot 5$ and in part 2 we wrote $9\left(1\right)$ . Both the dot and the parentheses tell us to multiply.

If you missed this problem, review the following video

Module 3: Integers