Solve the Linear Equation: 4x - 7 = 13 Step-by-Step

Q: What if I forget to do the same operation to both sides?

You'll get the wrong answer! The golden rule of equations is: whatever you do to one side, you must do to the other side. This keeps the equation balanced.

Q: How do I check if x = 5 is really correct?

Substitute 5 for x in the original equation: $ 4(5) - 7 = 20 - 7 = 13 $. Since this equals 13, our answer is correct!

Q: Why do we divide by 4 at the end?

Because we want x by itself, not 4x. When we have $ 4x = 20 $, dividing both sides by 4 gives us $ x = 5 $, which is our final answer.

Linear Equations with Integer Operations

$4x - 7 = 13$

$x = \text{?}$

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Understand the problem

$4x - 7 = 13$

$x = \text{?}$

Step-by-step solution

To solve the equation $4x - 7 = 13$ , follow these steps:

1. Add 7 to both sides: $4x = 13 + 7$

2. Simplify the right side: $4x = 20$

3. Divide both sides by 4: $x = \frac{20}{4}$

4. Solve: $x = 5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable term first
Technique: Add 7 to both sides: 4x - 7 + 7 = 13 + 7
Check: Substitute x = 5: 4(5) - 7 = 20 - 7 = 13 ✓

Common Mistakes

Avoid these frequent errors

Dividing by the coefficient before isolating the variable term
Don't divide 4x - 7 = 13 by 4 first = (x - 7/4 = 13/4)! This creates unnecessary fractions and makes the problem harder. Always add or subtract constants first to isolate the variable term, then divide.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I add 7 to both sides instead of subtracting?

Because we have -7 in the equation, and the inverse operation of subtraction is addition. Adding 7 cancels out the -7, leaving us with just $4x$ on the left side.

Can I subtract 13 from both sides first?

Technically yes, but it's not the most efficient approach. You'd get $4x - 20 = 0$ , then $4x = 20$ . It's easier to eliminate the constant term on the variable side first.

What if I forget to do the same operation to both sides?

You'll get the wrong answer! The golden rule of equations is: whatever you do to one side, you must do to the other side. This keeps the equation balanced.

How do I check if x = 5 is really correct?

Substitute 5 for x in the original equation: $4(5) - 7 = 20 - 7 = 13$ . Since this equals 13, our answer is correct!

Why do we divide by 4 at the end?

Because we want x by itself, not 4x. When we have $4x = 20$ , dividing both sides by 4 gives us $x = 5$ , which is our final answer.

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