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

A. [tex]$2x + 3 = 71$[/tex]
B. [tex]$2x + 3x = 71$[/tex]
C. [tex]$11x - 6 = 71$[/tex]
D. [tex]$7x - 6 = 71$[/tex]

To solve each of the given equations for [tex]$x$[/tex], let's go through them one by one:

1. Equation: [tex]$2x + 3 = 71$[/tex]

- Step 1: Subtract 3 from both sides to isolate the term with [tex]$x$[/tex].
[tex]\[
2x = 71 - 3
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
2x = 68
\][/tex]
- Step 3: Divide both sides by 2 to solve for [tex]$x$[/tex].
[tex]\[
x = \frac{68}{2} = 34
\][/tex]

2. Equation: [tex]$2x + 3x = 71$[/tex]

- Step 1: Combine like terms on the left-hand side.
[tex]\[
5x = 71
\][/tex]
- Step 2: Divide both sides by 5 to solve for [tex]$x$[/tex].
[tex]\[
x = \frac{71}{5} = 14.2
\][/tex]

3. Equation: [tex]$11x - 6 = 71$[/tex]

- Step 1: Add 6 to both sides to isolate the term with [tex]$x$[/tex].
[tex]\[
11x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
11x = 77
\][/tex]
- Step 3: Divide both sides by 11 to solve for [tex]$x$[/tex].
[tex]\[
x = \frac{77}{11} = 7
\][/tex]

4. Equation: [tex]$7x - 6 = 71$[/tex]

- Step 1: Add 6 to both sides to isolate the term with [tex]$x$[/tex].
[tex]\[
7x = 71 + 6
\][/tex]
- Step 2: Simplify the right-hand side.
[tex]\[
7x = 77
\][/tex]
- Step 3: Divide both sides by 7 to solve for [tex]$x$[/tex].
[tex]\[
x = \frac{77}{7} = 11
\][/tex]

Based on these solutions, the equations can be solved for [tex]$x$[/tex] as follows:
- [tex]$x = 34$[/tex] for the equation [tex]$2x + 3 = 71$[/tex]
- [tex]$x = 14.2$[/tex] for the equation [tex]$2x + 3x = 71$[/tex]
- [tex]$x = 7$[/tex] for the equation [tex]$11x - 6 = 71$[/tex]
- [tex]$x = 11$[/tex] for the equation [tex]$7x - 6 = 71$[/tex]