 ## How to Use Integers to Complete Equations?

To use integers in equations, it's essential to know the rules of operations (addition, subtraction, multiplication, and division) for integers. Here's how to complete equations involving integers:

• If both integers are positive, simply add the numbers as you would normally.
• If both integers are negative, add the numbers and place a negative sign before your answer.
• If one integer is positive and the other is negative, subtract the numbers (ignoring the signs) and use the sign of the number with the larger absolute value.

### Subtraction:

• When subtracting integers, change the operation to addition and add the additive inverse (opposite) of the second number. In other words, if you're trying to calculate $$a - b$$, think of it as $$a + (-b)$$.

### Multiplication & Division:

• If both integers are positive or both are negative, the result will be positive.
• If one integer is positive and the other is negative, the result will be negative.

With these rules in mind, you can solve equations that involve integers. Here are some examples:

### Example 1: Solve the equation $$x - 3 = 7$$ for $$x$$.

To solve for $$x$$, add $$3$$ to both sides of the equation to isolate $$x$$ on one side: $$x = 7 + 3$$, hence $$x = 10$$.

### Example 2: Solve the equation $$-2x = 16$$ for $$x$$.

To solve for $$x$$, divide both sides by $$-2$$: $$x = 16 / -2$$, hence $$x = -8$$.

### Example 3: Solve the equation $$5x - 7 = 18$$ for $$x$$.

First, add $$7$$ to both sides to isolate the term with $$x$$: $$5x = 18 + 7$$, hence $$5x = 25$$. Then, divide by $$5$$ to solve for $$x$$: $$x = 25 / 5$$, so $$x = 5$$.

Remember to always perform the same operation on both sides of the equation to maintain equality.

### Exercises for Use Integers to Complete Equations

1) $$x \ - \ 2 = 10$$$$\ \Rightarrow \$$

2) $$x \ - \ 5 = 3$$$$\ \Rightarrow \$$

3) $$x \ + \ 4 = 5$$$$\ \Rightarrow \$$

4) $$x \ + \ 2 = -2$$$$\ \Rightarrow \$$

5) $$x \ - \ 4 = 4$$$$\ \Rightarrow \$$

6) $$x \ - \ 4 = 11$$$$\ \Rightarrow \$$

7) $$x \ - \ 5 = -4$$$$\ \Rightarrow \$$

8) $$x \ - \ 2 = -3$$$$\ \Rightarrow \$$

9) $$x \ + \ 4 = -8$$$$\ \Rightarrow \$$

10) $$x \ + \ 4 = 6$$$$\ \Rightarrow \$$

1) $$x \ - \ 2 = 10$$$$\ \Rightarrow \ \color{red}{x = 10 \ + \ 2 = 12}$$
2) $$x \ - \ 5 = 3$$$$\ \Rightarrow \ \color{red}{x = 3 \ + \ 5 = 8}$$
3) $$x \ + \ 4 = 5$$$$\ \Rightarrow \ \color{red}{x = 5 \ - \ 4 = 1}$$
4) $$x \ + \ 2 = -2$$$$\ \Rightarrow \ \color{red}{x = -2 \ - \ 2 = -4}$$
5) $$x \ - \ 4 = 4$$$$\ \Rightarrow \ \color{red}{x = 4 \ + \ 4 = 8}$$
6) $$x \ - \ 4 = 11$$$$\ \Rightarrow \ \color{red}{x = 11 \ + \ 4 = 15}$$
7) $$x \ - \ 5 = -4$$$$\ \Rightarrow \ \color{red}{x = -4 \ + \ 5 = 1}$$
8) $$x \ - \ 2 = -3$$$$\ \Rightarrow \ \color{red}{x = -3 \ + \ 2 = -1}$$
9) $$x \ + \ 4 = -8$$$$\ \Rightarrow \ \color{red}{x = -8 \ - \ 4 = -12}$$
10) $$x \ + \ 4 = 6$$$$\ \Rightarrow \ \color{red}{x = 6 \ - \ 4 = 2}$$

## Use Integers to Complete Equations Practice Quiz

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