Solve the Linear Equation: Isolating X in 7x = 4

Q: Why do I need to divide both sides by 7?

To keep the equation balanced! Whatever you do to one side, you must do to the other side. If you only divide the left side by 7, the equation becomes unequal.

Q: Is x = 4/7 really the final answer?

Yes! Fractional answers are completely normal in algebra. Since 4/7 is already in simplest form, this is your final answer.

Q: How can I check if x = 4/7 is correct?

Substitute it back: $ 7 \times \frac{4}{7} = \frac{28}{7} = 4 $. Since this equals the right side, your answer is correct!

Q: What if the coefficient was negative, like -7x = 4?

Same process! Divide both sides by -7: x = -4/7. The negative sign just changes the sign of your answer.

Q: Can I convert 4/7 to a decimal?

You could (4/7 ≈ 0.571), but exact fractions are usually preferred in algebra unless specifically asked for a decimal approximation.

Linear Equations with Division Method

Solve for X:

$7x=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this problem.

00:06 First, we need to get the unknown X by itself.

00:10 We'll adjust the equation to have X on one side.

00:16 Next, we'll simplify it as much as possible.

00:20 And there we have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$7x=4$

Step-by-step solution

To solve the equation $7x = 4$ , we will follow these steps:

Step 1: We start with the equation $7x = 4$ .
Step 2: Our goal is to isolate $x$ . Since $x$ is multiplied by 7, we will divide both sides of the equation by 7.
Step 3: Performing division: $x = \frac{4}{7}$

Therefore, the solution to the equation $7x = 4$ is $x = \frac{4}{7}$ .

Final Answer

$\frac{4}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both sides by coefficient to isolate variable
Technique: From 7x = 4, divide both sides: x = 4/7
Check: Substitute back: 7 × (4/7) = 4 ✓

Common Mistakes

Avoid these frequent errors

Dividing only one side by the coefficient
Don't divide just 7x by 7 and leave 4 unchanged = x = 4! This breaks the equality and gives completely wrong answers. Always divide both sides of the equation by the same number to maintain balance.

Practice Quiz

Test your knowledge with interactive questions

$\frac{-y}{5}=-25$

FAQ

Everything you need to know about this question

Why do I need to divide both sides by 7?

To keep the equation balanced! Whatever you do to one side, you must do to the other side. If you only divide the left side by 7, the equation becomes unequal.

Is x = 4/7 really the final answer?

Yes! Fractional answers are completely normal in algebra. Since 4/7 is already in simplest form, this is your final answer.

How can I check if x = 4/7 is correct?

Substitute it back: $7 \times \frac{4}{7} = \frac{28}{7} = 4$ . Since this equals the right side, your answer is correct!

What if the coefficient was negative, like -7x = 4?

Same process! Divide both sides by -7: x = -4/7. The negative sign just changes the sign of your answer.

Can I convert 4/7 to a decimal?

You could (4/7 ≈ 0.571), but exact fractions are usually preferred in algebra unless specifically asked for a decimal approximation.

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