College

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]7x - 6 = 71[/tex]
D. [tex]11x - 6 = 71[/tex]

Solve for [tex]x[/tex].
[tex]x =[/tex]

Answer :

Let's solve each equation step-by-step to find the value of [tex]\( x \)[/tex].

1. First Equation: [tex]\( 2x + 3 = 71 \)[/tex]
- Start by isolating [tex]\( 2x \)[/tex]. Subtract 3 from both sides:
[tex]\[
2x = 71 - 3
\][/tex]
[tex]\[
2x = 68
\][/tex]
- To find [tex]\( x \)[/tex], divide both sides by 2:
[tex]\[
x = \frac{68}{2}
\][/tex]
[tex]\[
x = 34
\][/tex]

2. Second Equation: [tex]\( 2x + 3x = 71 \)[/tex]
- First, combine like terms [tex]\( 2x + 3x \)[/tex] to get [tex]\( 5x \)[/tex]:
[tex]\[
5x = 71
\][/tex]
- Then, divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{71}{5}
\][/tex]
[tex]\[
x = 14.2
\][/tex]

3. Third Equation: [tex]\( 7x - 6 = 71 \)[/tex]
- Start by getting [tex]\( 7x \)[/tex] on its own. Add 6 to both sides:
[tex]\[
7x = 71 + 6
\][/tex]
[tex]\[
7x = 77
\][/tex]
- Divide both sides by 7 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{77}{7}
\][/tex]
[tex]\[
x = 11
\][/tex]

4. Fourth Equation: [tex]\( 11x - 6 = 71 \)[/tex]
- First, add 6 to both sides to isolate [tex]\( 11x \)[/tex]:
[tex]\[
11x = 71 + 6
\][/tex]
[tex]\[
11x = 77
\][/tex]
- Divide both sides by 11 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{77}{11}
\][/tex]
[tex]\[
x = 7
\][/tex]

In summary, the solutions for [tex]\( x \)[/tex] are:
- For [tex]\( 2x + 3 = 71 \)[/tex], [tex]\( x = 34 \)[/tex]
- For [tex]\( 2x + 3x = 71 \)[/tex], [tex]\( x = 14.2 \)[/tex]
- For [tex]\( 7x - 6 = 71 \)[/tex], [tex]\( x = 11 \)[/tex]
- For [tex]\( 11x - 6 = 71 \)[/tex], [tex]\( x = 7 \)[/tex]

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