Question
Solve the following equation by using the addition principle. Check the solution. \( 13=\mathrm{a}-7.1 \) The solution is \( a=\square \). (Type an integer or a decimal.)
Ask by Lynch Chadwick. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a = 20.1 \)
Solution
We start with the equation:
13 = a - 7.1
To isolate a using the addition principle, add 7.1 to both sides:
13 + 7.1 = a - 7.1 + 7.1
This simplifies to:
20.1 = a
So, a = 20.1.
Checking the solution by substituting a back into the original equation:
20.1 - 7.1 = 13
13 = 13
Since both sides match, our solution is correct.
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Simplify this solution Beyond the Answer
To solve the equation \( 13 = \mathrm{a} - 7.1 \) using the addition principle, we need to isolate \( a \). We can do this by adding \( 7.1 \) to both sides of the equation: \[ 13 + 7.1 = \mathrm{a} - 7.1 + 7.1 \] This simplifies to: \[ 20.1 = \mathrm{a} \] So, the solution is \( a = 20.1 \). Now, let's check the solution by substituting \( a \) back into the original equation: \[ 13 = 20.1 - 7.1 \] Calculating the right side gives: \[ 20.1 - 7.1 = 13 \] Since both sides of the equation are equal, our solution \( a = 20.1 \) is correct.
