How to Use Integers to Complete Equations

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.

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