Question
Perform this operation. \[ \begin{aligned}-14-m & =-52 \\ 14-14-m & =\square-52\end{aligned} \]
Ask by Vaughn Barker. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( m = 38 \) and \( \square = 14 \).
Solution
Solve the equation by following steps:
- step0: Solve for \(m\):
\(-14-m=-52\)
- step1: Move the constant to the right side:
\(-m=-52+14\)
- step2: Add the numbers:
\(-m=-38\)
- step3: Change the signs:
\(m=38\)
Solve the equation \( 14-14-m=x-52 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(14-14-m=x-52\)
- step1: Simplify:
\(-m=x-52\)
- step2: Swap the sides:
\(x-52=-m\)
- step3: Move the constant to the right side:
\(x=-m+52\)
Let's solve the given system of equations step by step.
1. **First Equation:**
\[
-14 - m = -52
\]
To isolate \( m \), we can add 14 to both sides:
\[
-m = -52 + 14
\]
Simplifying the right side:
\[
-m = -38
\]
Now, multiplying both sides by -1 gives:
\[
m = 38
\]
2. **Second Equation:**
\[
14 - 14 - m = \square - 52
\]
Simplifying the left side:
\[
-m = \square - 52
\]
To isolate \( \square \), we can add \( m \) to both sides:
\[
\square = -m + 52
\]
Now substituting \( m = 38 \) into the equation:
\[
\square = -38 + 52
\]
Simplifying this gives:
\[
\square = 14
\]
### Final Results:
- \( m = 38 \)
- \( \square = 14 \)
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Simplify this solution The Deep Dive
To solve the first equation \(-14 - m = -52\), let's isolate \(m\): 1. Add \(14\) to both sides: \[ -m = -52 + 14 \] \[ -m = -38 \] 2. Multiply both sides by \(-1\): \[ m = 38 \] Now let's substitute \(m = 38\) into the second equation \(14 - 14 - m = \square - 52\): 1. Replace \(m\) with \(38\): \[ 14 - 14 - 38 = \square - 52 \] \[ 0 - 38 = \square - 52 \] \[ -38 = \square - 52 \] 2. Add \(52\) to both sides: \[ -38 + 52 = \square \] \[ 14 = \square \] Thus, the value for the square is \(14\). In summary: \[ m = 38 \quad \text{and} \quad \square = 14 \]
