Question

Solve the following problem in two different ways: -3 [ n + 1/4 ] = 17.25. Explain why both strategies work to solve for n. Use both sketch features to show your work for both strategies. Input your solution and explanation below.

Answer 1

To solve the equation -3(n + 1/4) = 17.25, you can use either the strategy of distributing the -3 or isolating the variable n. Both strategies work because they follow the properties of equality.

Step-by-step explanation:

To solve the equation -3(n + 1/4) = 17.25, we can use two different strategies. The first strategy is to distribute -3 to both terms inside the parentheses and then simplify the equation. The second strategy is to isolate the variable n by adding 3(n + 1/4) to both sides of the equation. Both strategies work because they follow the properties of equality.

Strategy 1:

-3(n + 1/4) = 17.25

-3n - 3/4 = 17.25

-3n = 17.25 + 3/4

-3n = 18

n = 18 / -3

n = -6

Strategy 2:

-3(n + 1/4) = 17.25

-3n - 3/4 = 17.25

-3n = 17.25 + 3/4

-3n = 17.25 + 0.75

-3n = 18

n = 18 / -3

n = -6