Question

4 match each pair of equations with the move that turned the first equation into the second.
a. $4x + 9 = 4x - 3$
$2x + 9 = -3$
1 multiply both sides by $\frac{1}{4}$
b. $-4(5x - 7) = -18$
$5x - 7 = 4.5$

1. multiply both sides by $-4$

c. $8 - 10x = 7 + 5x$
$4 - 10x = 3 + 5x$

1. multiply both sides by $\frac{1}{4}$

d. $\frac{5x}{4} = -9$
$5x = -36$

1. add $-4x$ to both sides
2. add $-4$ to both sides.

5 $12x + 4 = 20x + 24$
$3x + 1 = 5x + 6$
select all the situations for which only zero or positive solutions make sense.
a. measuring temperature in degrees celsius at an arctic outpost each day in january.

Explanation:

Step1: Match A to its transformation

First equation: $6x + 9 = 4x - 3$; Second equation: $2x + 9 = -3$.
Subtract $4x$ (add $-4x$) to both sides:
$6x + 9 - 4x = 4x - 3 - 4x$
$\implies 2x + 9 = -3$
Matches 4. Add $-4x$ to both sides.

Step2: Match B to its transformation

First equation: $-4(5x - 7) = -18$; Second equation: $5x - 7 = 4.5$.
Multiply both sides by $-\frac{1}{4}$:
$-\frac{1}{4} \times [-4(5x - 7)] = -\frac{1}{4} \times (-18)$
$\implies 5x - 7 = 4.5$
Matches 1. Multiply both sides by $-\frac{1}{4}$.

Step3: Match C to its transformation

First equation: $8 - 10x = 7 + 5x$; Second equation: $4 - 10x = 3 + 5x$.
Add $-4$ to both sides:
$8 - 10x - 4 = 7 + 5x - 4$
$\implies 4 - 10x = 3 + 5x$
Matches 5. Add $-4$ to both sides.

Step4: Match D to its transformation

First equation: $\frac{5x}{-4} = 4$; Second equation: $5x = -16$.
Multiply both sides by $-4$:
$-4 \times \frac{5x}{-4} = -4 \times 4$
$\implies 5x = -16$
Matches 2. Multiply both sides by $-4$.

Step5: Match E to its transformation

First equation: $12x + 4 = 20x + 24$; Second equation: $3x + 1 = 5x + 6$.
Multiply both sides by $\frac{1}{4}$:
$\frac{1}{4}(12x + 4) = \frac{1}{4}(20x + 24)$
$\implies 3x + 1 = 5x + 6$
Matches 3. Multiply both sides by $\frac{1}{4}$.

Step6: Analyze the second question

For the situation "Measuring temperature in degrees Celsius at an Arctic outpost each day in January": Arctic temperatures in January are often negative, so zero/positive only does NOT make sense. (Note: The full list of options is cut off, but for the visible option, this is the analysis.)

Answer:

1. Equation matches:

• A → 4. Add -4x to both sides
• B → 1. Multiply both sides by $-\frac{1}{4}$
• C → 5. Add -4 to both sides
• D → 2. Multiply both sides by -4
• E → 3. Multiply both sides by $\frac{1}{4}$

1. For the visible temperature situation: This does NOT fit (negative values are valid here).