Answer :
Sure! Let's solve each equation step-by-step to see which one gives the same solution as the equation [tex]\(6m - 38 = 176\)[/tex].
1. Equation: [tex]\(6m - 38 = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m = 176 + 38
\][/tex]
[tex]\[
6m = 214
\][/tex]
[tex]\[
m = \frac{214}{6} \approx 35.67
\][/tex]
2. Equation: [tex]\(6m + 38 = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m = 176 - 38
\][/tex]
[tex]\[
6m = 138
\][/tex]
[tex]\[
m = \frac{138}{6} = 23
\][/tex]
3. Equation: [tex]\(6(m + 38) = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m + 228 = 176
\][/tex]
[tex]\[
6m = 176 - 228
\][/tex]
[tex]\[
6m = -52
\][/tex]
[tex]\[
m = \frac{-52}{6} \approx -8.67
\][/tex]
4. Equation: [tex]\(6(m - 38) = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m - 228 = 176
\][/tex]
[tex]\[
6m = 176 + 228
\][/tex]
[tex]\[
6m = 404
\][/tex]
[tex]\[
m = \frac{404}{6} \approx 67.33
\][/tex]
Now, let's compare the solutions:
- From the original equation [tex]\(6m - 38 = 176\)[/tex], we found [tex]\(m \approx 35.67\)[/tex].
- The only equation that gives the same solution as the original equation (approximately 35.67) is indeed the original equation itself: [tex]\(6m - 38 = 176\)[/tex]. None of the other equations provide this solution.
1. Equation: [tex]\(6m - 38 = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m = 176 + 38
\][/tex]
[tex]\[
6m = 214
\][/tex]
[tex]\[
m = \frac{214}{6} \approx 35.67
\][/tex]
2. Equation: [tex]\(6m + 38 = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m = 176 - 38
\][/tex]
[tex]\[
6m = 138
\][/tex]
[tex]\[
m = \frac{138}{6} = 23
\][/tex]
3. Equation: [tex]\(6(m + 38) = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m + 228 = 176
\][/tex]
[tex]\[
6m = 176 - 228
\][/tex]
[tex]\[
6m = -52
\][/tex]
[tex]\[
m = \frac{-52}{6} \approx -8.67
\][/tex]
4. Equation: [tex]\(6(m - 38) = 176\)[/tex]
To solve for [tex]\(m\)[/tex]:
[tex]\[
6m - 228 = 176
\][/tex]
[tex]\[
6m = 176 + 228
\][/tex]
[tex]\[
6m = 404
\][/tex]
[tex]\[
m = \frac{404}{6} \approx 67.33
\][/tex]
Now, let's compare the solutions:
- From the original equation [tex]\(6m - 38 = 176\)[/tex], we found [tex]\(m \approx 35.67\)[/tex].
- The only equation that gives the same solution as the original equation (approximately 35.67) is indeed the original equation itself: [tex]\(6m - 38 = 176\)[/tex]. None of the other equations provide this solution.
