Solve the Linear Equation: a-5=10 Step by Step

Q: Why do I add 5 instead of subtract 5?

You want to undo the subtraction of 5. Since the equation shows $ a - 5 $, you need to add 5 to both sides to cancel out the -5 and isolate a.

Q: What if I accidentally subtract 5 from both sides?

You'd get $ a - 10 = 5 $, which is wrong! Remember: do the opposite operation to what you see. If you see subtraction, add. If you see addition, subtract.

Q: How do I check if a = 15 is correct?

Substitute 15 back into the original equation: $ 15 - 5 = 10 $. Since $ 10 = 10 $ is true, your answer is correct!

Q: Do I always add to both sides when solving equations?

Not always! You use the opposite operation. If the equation has $ +5 $, you subtract 5. If it has $ -5 $, you add 5. Always do the opposite to isolate the variable.

Q: What does it mean to isolate the variable?

Isolating means getting the variable by itself on one side of the equation. So $ a = 15 $ shows a is isolated, telling us exactly what a equals.

Linear Equations with Addition Property

Solve for A:

$a-5=10$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for A:

$a-5=10$

Step-by-step solution

To solve for $a$ , we need to isolate it on one side of the equation. Starting with:

$a-5=10$

Add $5$ to both sides to get:

$a-5+5=10+5$

This simplifies to:

$a=15$

Therefore, the solution is $a = 15$ .

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

Addition Property: Add the same number to both sides of equation
Technique: Add 5 to both sides: a - 5 + 5 = 10 + 5
Check: Substitute back: 15 - 5 = 10, which equals 10 ✓

Common Mistakes

Avoid these frequent errors

Adding 5 to only one side of the equation
Don't add 5 to just the left side getting a = 0! This breaks the balance of the equation and gives completely wrong answers. Always add the same number to both sides to maintain equality.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I add 5 instead of subtract 5?

You want to undo the subtraction of 5. Since the equation shows $a - 5$ , you need to add 5 to both sides to cancel out the -5 and isolate a.

What if I accidentally subtract 5 from both sides?

You'd get $a - 10 = 5$ , which is wrong! Remember: do the opposite operation to what you see. If you see subtraction, add. If you see addition, subtract.

How do I check if a = 15 is correct?

Substitute 15 back into the original equation: $15 - 5 = 10$ . Since $10 = 10$ is true, your answer is correct!

Do I always add to both sides when solving equations?

Not always! You use the opposite operation. If the equation has $+5$ , you subtract 5. If it has $-5$ , you add 5. Always do the opposite to isolate the variable.

What does it mean to isolate the variable?

Isolating means getting the variable by itself on one side of the equation. So $a = 15$ shows a is isolated, telling us exactly what a equals.

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