Answer :
Sure, let's solve the expression step-by-step.
We need to simplify the expression: [tex]\(7(x - 3) + 12(x + 15)\)[/tex].
1. Distribute the 7 across the first parenthesis:
[tex]\[
7(x - 3) = 7 \times x - 7 \times 3 = 7x - 21
\][/tex]
2. Distribute the 12 across the second parenthesis:
[tex]\[
12(x + 15) = 12 \times x + 12 \times 15 = 12x + 180
\][/tex]
3. Combine like terms from both parts:
[tex]\[
(7x - 21) + (12x + 180) = 7x + 12x - 21 + 180
\][/tex]
4. Simplify by combining the like terms:
[tex]\[
7x + 12x = 19x \quad \text{(combining the x terms)}
\][/tex]
[tex]\[
-21 + 180 = 159 \quad \text{(combining the constant terms)}
\][/tex]
5. Write the final simplified expression:
[tex]\[
19x + 159
\][/tex]
So, the equivalent expression is [tex]\(19x + 159\)[/tex]. The correct answer is option B.
We need to simplify the expression: [tex]\(7(x - 3) + 12(x + 15)\)[/tex].
1. Distribute the 7 across the first parenthesis:
[tex]\[
7(x - 3) = 7 \times x - 7 \times 3 = 7x - 21
\][/tex]
2. Distribute the 12 across the second parenthesis:
[tex]\[
12(x + 15) = 12 \times x + 12 \times 15 = 12x + 180
\][/tex]
3. Combine like terms from both parts:
[tex]\[
(7x - 21) + (12x + 180) = 7x + 12x - 21 + 180
\][/tex]
4. Simplify by combining the like terms:
[tex]\[
7x + 12x = 19x \quad \text{(combining the x terms)}
\][/tex]
[tex]\[
-21 + 180 = 159 \quad \text{(combining the constant terms)}
\][/tex]
5. Write the final simplified expression:
[tex]\[
19x + 159
\][/tex]
So, the equivalent expression is [tex]\(19x + 159\)[/tex]. The correct answer is option B.
