Q. \(16 + 8 \cdot 5x = 56\)
Answer
Interpret the equation as \(16+8\cdot 5x=56\).
Simplify: \(16+40x=56\).
Subtract \(16\): \(40x=40\).
Divide by \(40\): \(x=1\).
Final result: \(x=1\)
Detailed Explanation
Problem: Solve the equation
\[
16 + 8\cdot 5x = 56.
\]
Step 1: Rewrite the equation clearly.
Make sure multiplication is understood as \(8\cdot 5x\). So we have:
\[
16 + 8\cdot 5x = 56.
\]
Step 2: Combine the constants multiplying \(x\).
Compute \(8\cdot 5\):
\[
8\cdot 5 = 40.
\]
Substitute this back into the equation:
\[
16 + 40x = 56.
\]
Step 3: Subtract \(16\) from both sides.
This isolates the term with \(x\):
\[
16 + 40x – 16 = 56 – 16.
\]
Simplify:
\[
40x = 40.
\]
Step 4: Divide both sides by \(40\).
This solves for \(x\):
\[
\frac{40x}{40} = \frac{40}{40}.
\]
Simplify:
\[
x = 1.
\]
Answer: \(\boxed{1}\)
See full solution
Algebra FAQ
How do I solve \(16+8\cdot 5x=56\)?
Subtract 16: \(8\cdot 5x=40\). Then \(40x=40\). So \(x=1\).
Why does \(8\cdot 5x\) become \(40x\)?
Because \(8\cdot 5=40\) and \(x\) multiplies the whole product: \(8\cdot 5x=(8\cdot 5)x=40x\).
What if the equation is written \(16+8(5x)=56\), do I still get \(x=1\)?
Yes. Use \(8(5x)=40x\). Then \(16+40x=56\). Subtract 16: \(40x=40\). So \(x=1\).
What is the quickest first step for \(16+8\cdot 5x=56\)?
Remove the constant: \(8\cdot 5x=56-16\). That gives \(8\cdot 5x=40\), then solve \(x\).
How do I check the solution \(x=1\) in the original equation?
Substitute: \(16+8\cdot 5(1)=16+40=56\). Since LHS \(=56\), the solution is correct.
What does “distributive property” mean here?
It means \(8\cdot (5x)=(8\cdot 5)x\). So \(16+8(5x)=16+40x\).
Try solving: 16+8+5x=56.
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