Answer :
To find the correct equation that represents the given situation, we need to carefully translate the words into a mathematical equation.
The problem states that "3 more than 8 times a number [tex]\( x \)[/tex] is equal to 83." Let's break this down step-by-step:
1. Identify the components:
- "8 times a number [tex]\( x \)[/tex]" is written mathematically as [tex]\( 8x \)[/tex].
- "3 more than" indicates adding 3 to the expression.
2. Combine these components:
- When you add 3 to [tex]\( 8x \)[/tex], you get [tex]\( 8x + 3 \)[/tex].
3. Set up the equation:
- The problem states that this expression is equal to 83. So we set up the equation as:
[tex]\[
8x + 3 = 83
\][/tex]
Let's check the given options to see which one corresponds to the equation we formed:
A. [tex]\((3)(8)x = 83\)[/tex] which simplifies to [tex]\(24x = 83\)[/tex] — incorrect.
B. [tex]\(8x = 83 + 3\)[/tex] which simplifies to [tex]\(8x = 86\)[/tex] — incorrect.
C. [tex]\(3x + 8 = 83\)[/tex] — incorrect.
D. [tex]\(8x + 3 = 83\)[/tex] — correct.
Therefore, the correct equation that represents this situation is:
[tex]\[
\boxed{8x + 3 = 83}
\][/tex]
The problem states that "3 more than 8 times a number [tex]\( x \)[/tex] is equal to 83." Let's break this down step-by-step:
1. Identify the components:
- "8 times a number [tex]\( x \)[/tex]" is written mathematically as [tex]\( 8x \)[/tex].
- "3 more than" indicates adding 3 to the expression.
2. Combine these components:
- When you add 3 to [tex]\( 8x \)[/tex], you get [tex]\( 8x + 3 \)[/tex].
3. Set up the equation:
- The problem states that this expression is equal to 83. So we set up the equation as:
[tex]\[
8x + 3 = 83
\][/tex]
Let's check the given options to see which one corresponds to the equation we formed:
A. [tex]\((3)(8)x = 83\)[/tex] which simplifies to [tex]\(24x = 83\)[/tex] — incorrect.
B. [tex]\(8x = 83 + 3\)[/tex] which simplifies to [tex]\(8x = 86\)[/tex] — incorrect.
C. [tex]\(3x + 8 = 83\)[/tex] — incorrect.
D. [tex]\(8x + 3 = 83\)[/tex] — correct.
Therefore, the correct equation that represents this situation is:
[tex]\[
\boxed{8x + 3 = 83}
\][/tex]
