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.
Free printable Worksheets
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
