Let's carefully analyze the problem and the options provided:
Anja represented the inequality [tex]\(\frac{4 - g}{8} \leq -15\)[/tex] with the phrase "the quotient of 4 minus a number and 8 is at least -15."
To understand Anja's error, let's dissect the meaning of each part of the phrase and the inequality:
1. The quotient of 4 minus a number and 8 - This correctly describes the left-hand side of the inequality [tex]\(\frac{4 - g}{8}\)[/tex].
2. is at least -15 - Here is where the error occurs. The phrase "at least -15" means [tex]\(\geq -15\)[/tex], but the inequality given is [tex]\(\leq -15\)[/tex], which means "at most -15."
Therefore, Anja should have described the inequality as "the quotient of 4 minus a number and 8 is at most -15," instead of "at least -15."
Let's review the provided options and see which one correctly identifies the error in Anja's statement:
1. Anja phrase should have stated "the difference of a number a - This is incomplete and does not address the specific error based on the relationship "at least -15."
2. Anja phrase should have stated "the quotient of a number an number and 8". - This is also incomplete and does not correct the specific phrasing error related to "at least -15."
3. Anja's phrase should have ended with "less than -15 ", not "at - This suggests a different comparative term but does not align with the mathematical relationship in the inequality.
4. Anja's phrase should have ended with "at most -15 ", not "at least -15." - This option correctly identifies the error. The inequality [tex]\(\leq -15\)[/tex] indeed means "at most -15," not "at least -15."
Hence, the correct option that describes Anja's error is:
Option 4: Anja's phrase should have ended with "at most -15," not "at least -15."
