Answer :
To solve this problem, we need to translate the statement "3 more than 8 times a number [tex]\( x \)[/tex] is equal to 83" into an algebraic equation. Let's break it down step by step:
1. Identify the components of the statement:
- "8 times a number [tex]\( x \)[/tex]" can be represented as [tex]\( 8x \)[/tex].
- "3 more than" this means we add 3 to the expression [tex]\( 8x \)[/tex].
2. Combine these components into a complete expression:
- Adding 3 to [tex]\( 8x \)[/tex] gives us [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:
[tex]\[
8x + 3 = 83
\][/tex]
4. Identify the correct choice:
- From the options provided:
- Option A suggests [tex]\( (3)(8) x = 83 \)[/tex], which is incorrect.
- Option B suggests [tex]\( 8x = 83 + 3 \)[/tex], which is incorrect.
- Option C suggests [tex]\( 3x + 8 = 83 \)[/tex], which is incorrect.
- Option D suggests [tex]\( 8x + 3 = 83 \)[/tex], which matches our equation.
Therefore, the correct equation that represents the situation is Option D: [tex]\( 8x + 3 = 83 \)[/tex].
1. Identify the components of the statement:
- "8 times a number [tex]\( x \)[/tex]" can be represented as [tex]\( 8x \)[/tex].
- "3 more than" this means we add 3 to the expression [tex]\( 8x \)[/tex].
2. Combine these components into a complete expression:
- Adding 3 to [tex]\( 8x \)[/tex] gives us [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:
[tex]\[
8x + 3 = 83
\][/tex]
4. Identify the correct choice:
- From the options provided:
- Option A suggests [tex]\( (3)(8) x = 83 \)[/tex], which is incorrect.
- Option B suggests [tex]\( 8x = 83 + 3 \)[/tex], which is incorrect.
- Option C suggests [tex]\( 3x + 8 = 83 \)[/tex], which is incorrect.
- Option D suggests [tex]\( 8x + 3 = 83 \)[/tex], which matches our equation.
Therefore, the correct equation that represents the situation is Option D: [tex]\( 8x + 3 = 83 \)[/tex].
