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Answer :
To solve the problem, we need to determine which equation corresponds to solving for [tex]\(x\)[/tex]. Let's look at the given equations:
1. [tex]\(2x - 49 = 83\)[/tex]
2. [tex]\(2x - 33 = 83\)[/tex]
3. [tex]\(2x + 33 = 83\)[/tex]
4. [tex]\(2x + 49 = 83\)[/tex]
Next, you need to solve each equation step-by-step to see which one gives a sensible solution for [tex]\(x\)[/tex].
Let's check the first equation:
1. [tex]\(2x - 49 = 83\)[/tex]
- Add 49 to both sides to get:
[tex]\[
2x - 49 + 49 = 83 + 49
\][/tex]
[tex]\[
2x = 132
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{132}{2}
\][/tex]
[tex]\[
x = 66
\][/tex]
The solution for [tex]\(x\)[/tex] is 66, which means the equation [tex]\(2x - 49 = 83\)[/tex] can indeed be used to solve for [tex]\(x\)[/tex]. Therefore, the equation to use is:
[tex]\[ 2x - 49 = 83 \][/tex]
And the solution to this equation for [tex]\(x\)[/tex] is:
[tex]\[ x = 66 \][/tex]
1. [tex]\(2x - 49 = 83\)[/tex]
2. [tex]\(2x - 33 = 83\)[/tex]
3. [tex]\(2x + 33 = 83\)[/tex]
4. [tex]\(2x + 49 = 83\)[/tex]
Next, you need to solve each equation step-by-step to see which one gives a sensible solution for [tex]\(x\)[/tex].
Let's check the first equation:
1. [tex]\(2x - 49 = 83\)[/tex]
- Add 49 to both sides to get:
[tex]\[
2x - 49 + 49 = 83 + 49
\][/tex]
[tex]\[
2x = 132
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{132}{2}
\][/tex]
[tex]\[
x = 66
\][/tex]
The solution for [tex]\(x\)[/tex] is 66, which means the equation [tex]\(2x - 49 = 83\)[/tex] can indeed be used to solve for [tex]\(x\)[/tex]. Therefore, the equation to use is:
[tex]\[ 2x - 49 = 83 \][/tex]
And the solution to this equation for [tex]\(x\)[/tex] is:
[tex]\[ x = 66 \][/tex]
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