Solve for X in the Linear Equation: 5x + 7 = 32

Q: Why do I subtract 7 instead of dividing by 5 first?

You need to follow the order of operations in reverse! Since 7 was added to 5x, you must subtract 7 first to undo that operation, then divide by 5.

Q: What if I get a negative number when I subtract?

That's completely normal! If you had $ 5x + 7 = 2 $, you'd get $ 5x = -5 $, so $ x = -1 $. Negative solutions are valid!

Q: What if my final answer has a decimal?

Decimal answers are perfectly fine! Just make sure to double-check your arithmetic and verify by substituting the decimal back into the original equation.

Linear Equations with Integer Solutions

$5x+7=32$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve the equation together.

00:07 First, we need to focus on getting X by itself.

00:11 We do this by moving everything else to the other side.

00:15 Now, X is all alone!

00:18 And there we have it, our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5x+7=32$

Step-by-step solution

To solve this linear equation, follow these steps:

Step 1: Isolate the term with $x$ by subtracting 7 from both sides of the equation.
Step 2: Perform the subtraction to simplify the equation.
Step 3: Divide both sides by 5 to solve for $x$ .

Let’s perform each step:

Step 1: Subtract 7 from both sides:
$5x + 7 - 7 = 32 - 7$

This simplifies to:
$5x = 25$

Step 2: Divide both sides by 5 to isolate $x$ :
$x = \frac{25}{5}$

Perform the division:
$x = 5$

Hence, the solution to the equation $5x + 7 = 32$ is $x = 5$ .

Final Answer

$x=5$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Use inverse operations to isolate the variable term first
Technique: Subtract 7 from both sides: 32 - 7 = 25
Check: Substitute back: 5(5) + 7 = 25 + 7 = 32 ✓

Common Mistakes

Avoid these frequent errors

Dividing before subtracting the constant term
Don't divide 5x + 7 = 32 by 5 to get x + 7/5 = 32/5! This creates messy fractions and complicates the problem unnecessarily. Always subtract or add constants first to isolate the variable term, then divide.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I subtract 7 instead of dividing by 5 first?

You need to follow the order of operations in reverse! Since 7 was added to 5x, you must subtract 7 first to undo that operation, then divide by 5.

What if I get a negative number when I subtract?

That's completely normal! If you had $5x + 7 = 2$ , you'd get $5x = -5$ , so $x = -1$ . Negative solutions are valid!

How do I know which operation to do first?

Think about what operations were done to x originally. If the equation shows 5x + 7, then x was multiplied by 5, then 7 was added. To solve, do the reverse: subtract 7 first, then divide by 5.

Can I check my answer a different way?

Yes! Besides substituting back, you can also think logically: if x = 5, then 5 times 5 equals 25, plus 7 equals 32. This matches the right side of the equation!

What if my final answer has a decimal?

Decimal answers are perfectly fine! Just make sure to double-check your arithmetic and verify by substituting the decimal back into the original equation.

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