Answer :
To solve this problem, we need to translate the verbal description into an algebraic equation. Let's break down the sentence given:
1. "8 times a number [tex]\( x \)[/tex]": This part can be written as [tex]\( 8x \)[/tex]. It means you're multiplying a number [tex]\( x \)[/tex] by 8.
2. "3 more than 8 times a number [tex]\( x \)[/tex]": This means you need to add 3 to the expression [tex]\( 8x \)[/tex], which gives us [tex]\( 8x + 3 \)[/tex].
3. "is equal to 83": This tells us that the expression we’ve formed ([tex]\( 8x + 3 \)[/tex]) is equal to 83.
Putting it all together, the equation representing the situation is:
[tex]\[ 8x + 3 = 83 \][/tex]
Thus, the correct choice is:
D) [tex]\( 8x + 3 = 83 \)[/tex]
1. "8 times a number [tex]\( x \)[/tex]": This part can be written as [tex]\( 8x \)[/tex]. It means you're multiplying a number [tex]\( x \)[/tex] by 8.
2. "3 more than 8 times a number [tex]\( x \)[/tex]": This means you need to add 3 to the expression [tex]\( 8x \)[/tex], which gives us [tex]\( 8x + 3 \)[/tex].
3. "is equal to 83": This tells us that the expression we’ve formed ([tex]\( 8x + 3 \)[/tex]) is equal to 83.
Putting it all together, the equation representing the situation is:
[tex]\[ 8x + 3 = 83 \][/tex]
Thus, the correct choice is:
D) [tex]\( 8x + 3 = 83 \)[/tex]
