High School

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------------------------------------------------ Which equation can be used to solve for [tex]$x$[/tex]?

A. [tex]2x - 49 = 83[/tex]
B. [tex]2x - 33 = 83[/tex]
C. [tex]2x + 33 = 83[/tex]
D. [tex]2x + 49 = 83[/tex]

Solve for [tex]$x$[/tex].
[tex]x = \square[/tex]

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]