Question: User: Question 6
(Multiple Choice Worth 2 Points)
(Properties of Operations MC)
Which of the following is equivalent to $-4(2x + 3y) - 18q - 42p$?
$-8x + 12y - 18q + 42p$
$-8x - 12y - 18q - 42p$
$-8x + 3y - 18q + 7p$
$-24(2x + 3y - 3q + 7p)$
Question 7
(Multiple Choice Worth 2 Points)
(Operations with Absolute Values MC)
What is the value of the absolute value expression $|-134| + |4| - |-35|$?
$-165$
$-95$
$173$
$103$
1. **Problem 1:** Simplify the expression $-4(2x + 3y) - 18q - 42p$ and find which option is equivalent.
2. Use the distributive property: $a(b + c) = ab + ac$.
3. Apply distributive property:
$$-4(2x + 3y) = -4 \times 2x + (-4) \times 3y = -8x - 12y$$
4. Substitute back:
$$-8x - 12y - 18q - 42p$$
5. Compare with options:
- Option 1: $-8x + 12y - 18q + 42p$ (signs differ)
- Option 2: $-8x - 12y - 18q - 42p$ (matches exactly)
- Option 3: $-8x + 3y - 18q + 7p$ (does not match)
- Option 4: $-24(2x + 3y - 3q + 7p)$ (not equivalent)
**Answer for Problem 1:** $-8x - 12y - 18q - 42p$
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6. **Problem 2:** Evaluate $|-134| + |4| - |-35|$.
7. Recall that absolute value $|a|$ is the distance from zero, always non-negative.
8. Calculate each absolute value:
$$|-134| = 134$$
$$|4| = 4$$
$$|-35| = 35$$
9. Substitute and simplify:
$$134 + 4 - 35 = 138 - 35 = 103$$
**Answer for Problem 2:** $103$