Q. Solve. \(2(2x-4)=4\)
Answer
\[
2(2x-4)=4
\]
\[
2x-4=2
\]
\[
2x=6
\]
\[
x=3
\]
Detailed Explanation
- Write the original equation.\(2(2x-4)=4\)
- Apply the distributive property to remove the parentheses.Multiply 2 by each term inside the parentheses: 2 times 2x is 4x, and 2 times −4 is −8.
\(2(2x-4)=4 \; \Rightarrow \; 4x-8=4\)
- Isolate the term with the variable by undoing the subtraction.Add 8 to both sides to eliminate the −8 on the left side. This keeps the equality balanced.
\(4x-8+8=4+8\)
Simplify both sides:
\(4x=12\)
- Solve for x by undoing the multiplication.Divide both sides by 4 to isolate x.
\(\dfrac{4x}{4}=\dfrac{12}{4}\)
Simplify:
\(x=3\)
- Check the solution by substituting back into the original equation.Substitute \(x=3\) into \(2(2x-4)\):
\(2\bigl(2\cdot 3 – 4\bigr)=2(6-4)=2\cdot 2=4\)
The left-hand side equals the right-hand side, so the solution is correct.
Solution: \(x=3\)
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Algebra FAQs
How do I start solving \(2(2x-4)=4\)?.
Use the distributive property: \(2(2x-4)=4x-8\). Then solve the resulting linear equation \(4x-8=4\).
What are the step-by-step operations to isolate \(x\)?.
Add 8 to both sides: \(4x=12\). Then divide by 4: \(x=3\)..
Can I check the solution works?
Substitute \(x=3\): \(2(2\cdot 3-4)=2(6-4)=2\cdot 2=4\). Both sides match, so \(x=3\) is correct.
Could I have divided both sides by 2 first?
Yes. Dividing by 2 gives \(2x-4=2\). Then add 4: \(2x=6\), divide by 2: \(x=3\).
What common mistakes should I avoid?
Forgetting to distribute, dropping signs (especially minus), dividing by the wrong number, or failing to check the solution.
What if the equation were \(2(2x-4)=0\)?
What if the equation were \(2(2x-4)=0\)?
Why do we perform inverse operations in that order?
We reverse the order of operations: undo addition/subtraction before multiplication/division on the variable term to isolate \(x\) correctly.
Is this an example of a linear equation?
Yes. After distribution it becomes \(4x-8=4\), a first-degree (linear) equation with one solution..
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