Solve for X in the Linear Equation: 7 - x = 15 - 5

Q: Why do I need to simplify 15 - 5 first?

Simplifying first makes the equation cleaner and easier to work with! $ 7 - x = 10 $ is much clearer than $ 7 - x = 15 - 5 $.

Q: What does 'isolate the variable' actually mean?

Isolating means getting x by itself on one side of the equation. You use inverse operations to 'undo' what's being done to x until it stands alone.

Q: Why is the answer negative?

When we get $ -x = 3 $, we have negative x equals 3. To find x, we divide both sides by -1, giving us $ x = -3 $.

Q: How do I check if x = -3 is correct?

Substitute back into the original equation: $ 7 - (-3) = 15 - 5 $. This gives us $ 7 + 3 = 10 $, so $ 10 = 10 $ ✓

Q: What if I accidentally add 7 instead of subtracting?

Adding 7 to both sides would give you $ 14 - x = 17 $, making the problem more complicated! Always use the opposite operation to cancel out terms.

Linear Equations with Simplification Steps

Solve for X:

$7 - x = 15 - 5$

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Understand the problem

Solve for X:

$7 - x = 15 - 5$

Step-by-step solution

First, simplify the right side of the equation:
$15 - 5 = 10$
Hence, the equation becomes $7 - x = 10$ .
Subtract 7 from both sides to isolate $x$ :
$7 - x - 7 = 10 - 7$
This simplifies to:
$-x=3$
Divide by -1 to solve for $x$ :
$x=-3$
Therefore, the solution is $x=-3$ .

Final Answer

-3

Key Points to Remember

Essential concepts to master this topic

Simplify first: Always combine like terms on each side before isolating variables
Technique: Subtract 7 from both sides: $-x = 3$
Check: Substitute $x = -3$ back: $7 - (-3) = 10$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify before solving
Don't jump straight to isolating x without simplifying 15 - 5 = 10 first! This creates unnecessary confusion and makes the problem harder than it needs to be. Always simplify both sides completely before applying inverse operations.

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 need to simplify 15 - 5 first?

Simplifying first makes the equation cleaner and easier to work with! $7 - x = 10$ is much clearer than $7 - x = 15 - 5$ .

What does 'isolate the variable' actually mean?

Isolating means getting x by itself on one side of the equation. You use inverse operations to 'undo' what's being done to x until it stands alone.

Why is the answer negative?

When we get $-x = 3$ , we have negative x equals 3. To find x, we divide both sides by -1, giving us $x = -3$ .

How do I check if x = -3 is correct?

Substitute back into the original equation: $7 - (-3) = 15 - 5$ . This gives us $7 + 3 = 10$ , so $10 = 10$ ✓

What if I accidentally add 7 instead of subtracting?

Adding 7 to both sides would give you $14 - x = 17$ , making the problem more complicated! Always use the opposite operation to cancel out terms.

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Solve for X in the Linear Equation: 7 - x = 15 - 5

Linear Equations with Simplification Steps

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to simplify 15 - 5 first?

What does 'isolate the variable' actually mean?

Why is the answer negative?

How do I check if x = -3 is correct?

What if I accidentally add 7 instead of subtracting?

🌟 Unlock Your Math Potential

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