Question

1. in △abc, ab = 18 and bc = 7. complete the inequality for the possible lengths of side ac.

11 < ac < 25

1. phil was asked to solve for x in the diagram below. he was told his answer is incorrect. phils

response:
6x + 24 = 60 + 60 + 60
6x + 24 = 180
x = 26
a. describe phils mistake.
set the equation
up wrong
b. what value of x should phil have
gotten?

Explanation:

Step1: Analyze Phil's equation

Phil set \(6x + 24=60 + 60+60\). But in an equilateral - triangle - related angle (assuming the figure is an equilateral - like angle - sum situation, the correct sum of angles for a straight - line or a triangle's supplementary angle should be \(180^{\circ}\)). He wrongly set the right - hand side as \(60 + 60+60\) instead of \(180\).

Step2: Solve the correct equation

We have the correct equation \(6x + 24 = 180\).
Subtract \(24\) from both sides: \(6x=180 - 24\).
So, \(6x = 156\).
Divide both sides by \(6\): \(x=\frac{156}{6}=26\).

Answer:

a. Phil wrongly set the right - hand side of the equation. Instead of using the correct sum (e.g., \(180^{\circ}\) for a straight - line angle), he used \(60 + 60+60\).
b. \(x = 26\)