## How to Use Integers to Complete Equations?

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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:

### Addition:

- 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) **\( x \ + \ 4 = 6 \)\( \ \Rightarrow \ \)