Question

Stella wants to build up her emergency fund to $10,000. she has $2,000 now and plans on saving $320 every month. to model the situation, she creates this equation, where x represents the number of months and y represents the total amount in her emergency fund: y = 2,000 320x. determine the missing steps and justifications in her work.

a) y − 2,000 = 2,000 320x − 2,000
b) Division property of equality
c) x = 25
d) x = 24
e) x = x
f) y − 2,000 = 2,000 − 320x − 2,000
g) Multiplication property of equality

Answer 1

To determine the missing steps and justifications in Stella's work, we need to evaluate each option and identify any incorrect steps and missing justifications.

Step-by-step explanation:

To determine the missing steps and justifications in Stella's work, let's go through each option:

a) y - 2,000 = 2,000 320x - 2,000 - This step is correct. It subtracts 2,000 from both sides of the equation.

b) Division property of equality - This step is missing. The division property of equality states that if you divide both sides of an equation by the same non-zero number, the equation remains true.

c) x = 25 - This step is incorrect. To solve for x, divide both sides of the equation by 320, not 2,000. The correct step would be y/320 - 2,000/320 = x, which simplifies to x = (y-2,000)/320.

d) x = 24 - This step is incorrect. It is not the correct solution to the equation.

e) x = x - This step is missing. It is not a necessary step in solving the equation.

f) y - 2,000 = 2,000 - 320x - 2,000 - This step is correct. It subtracts 2,000 - 320x from both sides of the equation.

g) Multiplication property of equality - This step is missing. The multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the equation remains true.

Therefore, the missing steps and justifications in Stella's work are:

b) Division property of equality,

c) x = (y-2,000)/320, and

g) Multiplication property of equality.