Question
Solve using the multiplication principle. Don't forget to check. \( 2 x=8 \)
Ask by Wheeler Weaver. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 4 \)
Solution
We start with the equation:
2x = 8
Step 1: Use the multiplication (or inverse multiplication) principle. Since 2 is multiplied by x, we can undo that multiplication by multiplying both sides of the equation by the reciprocal of 2, which is 1/2.
Multiplying both sides by 1/2 gives:
(1/2) · (2x) = (1/2) · 8
Step 2: Simplify the left-hand side:
(1/2) · 2x = (1) · x = x
The right-hand side simplifies to:
8/2 = 4
So, we have:
x = 4
Step 3: Check the solution by substituting x = 4 back into the original equation:
2(4) = 8
8 = 8
Since both sides are equal, the solution x = 4 is correct.
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Simplify this solution Beyond the Answer
To solve the equation \( 2x = 8 \) using the multiplication principle, we need to isolate \( x \). We can do this by dividing both sides of the equation by 2. So, \( x = \frac{8}{2} = 4 \). Now, let's check our solution by substituting \( x \) back into the original equation: \( 2(4) = 8 \). This is true, confirming that \( x = 4 \) is indeed correct!
