Solving One-Step Addition/Subtraction Equations

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Concept Review

Inverse Operations: The Undo Button for Math

Imagine you're playing a video game and you make a wrong move. What do you wish you had? An undo button! In mathematics, we have something just as powerful called inverse operations — they let us "undo" what's been done to a variable.

When solving equations, our goal is to get the variable (like x) all by itself on one side. Think of it like unwrapping a present — you need to carefully remove each layer to reveal what's inside.

The Addition and Subtraction Partnership

Addition and subtraction are perfect opposites — they're inverse operations. Addition puts numbers together, while subtraction takes them apart. When we see one operation "bothering" our variable, we use its inverse to cancel it out.

Solving Step-by-Step

Example: Solve x + 12 = 25

Step 1: Notice that 12 is being added to x

Step 2: Use the inverse operation — subtract 12 from both sides

Step 3: x + 12 - 12 = 25 - 12

Step 4: x = 13

The +12 and -12 cancel each other out, leaving x alone!

Let's try the opposite situation. If we have y - 8 = 15, then 8 is being subtracted from y. To undo subtraction, we add 8 to both sides: y - 8 + 8 = 15 + 8, so y = 23.

🔑 Key Insight

Whatever you do to one side of an equation, you must do to the other side. Think of an equation like a balanced scale — if you add weight to one side, you need to add the same weight to the other side to keep it balanced. This is why we always perform the same inverse operation on both sides.

The Golden Rule: Keep It Balanced

The equals sign (=) means both sides have the same value. When we use inverse operations to solve equations, we're like mathematical detectives, carefully removing clues while maintaining perfect balance. Each step brings us closer to isolating our variable and discovering its true value.

🎯 Key Takeaway

Just like that undo button in your favorite game, inverse operations give us the power to reverse mathematical steps and solve for unknown values. Master this concept, and you'll have the ultimate tool for unwrapping the mystery hidden in any one-step equation!

Sample questions

1. To solve x + 5 = 12, what inverse operation should you use?

○ Add 5 to both sides

○ Multiply both sides by 5

✓ Subtract 5 from both sides

○ Divide both sides by 5

Answer: Subtract 5 from both sides — Addition and subtraction are inverse operations. To undo adding 5, subtract 5.

2. What is the inverse operation of subtraction?

✓ Addition

○ Multiplication

○ Division

○ Exponents

Answer: Addition — Subtraction and addition undo each other.

3. To isolate the variable in y - 8 = 15, what should you do?

○ Subtract 8 from both sides

✓ Add 8 to both sides

○ Multiply by 8

○ Divide by 8

Answer: Add 8 to both sides — To undo subtracting 8, add 8 to both sides.

Skills in this topic

Understand the concept of inverse operations to isolate a variable
Solve equations of the form x + p = q for cases in which p, q and x are all nonnegative rational numbers
Solve equations of the form x - p = q
Check the solution to an equation by substituting it back into the original equation
Write and solve one-step addition or subtraction equations for real-world word problems

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