Question
Solve using the multiplication principle. Don't forget to perform a check. \( 7 x=-56 \)
Ask by Simpson Wilson. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -8 \)
Solution
We are given the equation:
7x = -56
Step 1: Use the multiplication principle. Here, 7 is multiplied by x. To find x, we need to reverse the multiplication by dividing both sides by 7.
Step 2: Divide both sides of the equation by 7:
(7x)/7 = (-56)/7
This simplifies to:
x = -56/7
Step 3: Compute -56 divided by 7:
x = -8
Verification (Check):
Substitute x = -8 back into the original equation:
7(-8) = -56
Since both sides are equal, the solution is confirmed.
The solution is: x = -8.
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Simplify this solution Extra Insights
To solve the equation \( 7x = -56 \) using the multiplication principle, you'll want to isolate \( x \). Divide both sides of the equation by 7: \[ x = \frac{-56}{7} \] This simplifies to \( x = -8 \). Now, let’s perform a quick check. Substitute \(-8\) back into the original equation: \[ 7(-8) = -56 \] Since this is true, your solution \( x = -8 \) is indeed correct! Keep in mind that the multiplication principle states that you can multiply or divide both sides of an equation by the same non-zero number, which is key to isolating the variable. Now you’ve aced it!
