Question

1. make each equation true by filling in the correct operation.

$48\square(-8) = -6$ $(-40)\square8 = -5$
$12\square(-2) = 14$ $18\square(-12) = 6$
problems 7–8: maneli and trinidad are trying to solve the equation $\frac{2}{3}$

• maneli says: i think we should multiply each side by $\frac{3}{2}$ because that is the of $\frac{2}{3}$.
• trinidad says: i think we should add $-\frac{2}{3}$ to each side because that is the

1. which person’s strategy should they use?

Explanation:

Step1: Solve first equation

Test operations: $48 \div (-8) = -6$, so operation is $\div$.

Step2: Solve second equation

Test operations: $(-40) \div 8 = -5$, so operation is $\div$.

Step3: Solve third equation

Test operations: $12 - (-2) = 14$, so operation is $-$.

Step4: Solve fourth equation

Test operations: $18 + (-12) = 6$, so operation is $+$.

Step5: Analyze Problem 7 logic

Maneli refers to reciprocal for multiplication, Trinidad to additive inverse. The equation is $\frac{2}{3}x = \text{[value]}$ (implied), so multiply by reciprocal $\frac{3}{2}$.

Answer:

For Problem 6:

1. $48 \boldsymbol{\div} (-8) = -6$
2. $(-40) \boldsymbol{\div} 8 = -5$
3. $12 \boldsymbol{-} (-2) = 14$
4. $18 \boldsymbol{+} (-12) = 6$

For Problem 7:
They should use Maneli's strategy, as multiplying by the reciprocal of $\frac{2}{3}$ is the correct method to solve an equation where $x$ is multiplied by $\frac{2}{3}$, while adding the additive inverse is used to undo addition, not multiplication.