To determine which inequality Hessa solved to result in the dot at 5, we need to solve each inequality to see which one yields \( x = 5 \). Let's consider each option step by step:
**Option A: \( \frac{3}{7}x + \frac{1}{7} < 1 \frac{6}{7} \)**
First, convert \( 1 \frac{6}{7} \) to an improper fraction:
\[ 1 \frac{6}{7} = \frac{13}{7} \]
The inequality becomes:
\[ \frac{3}{7}x + \frac{1}{7} < \frac{13}{7} \]
Subtract \( \frac{1}{7} \) from both sides:
\[ \frac{3}{7}x < \frac{13}{7} - \frac{1}{7} \]
\[ \frac{3}{7}x < \frac{12}{7} \]
Multiply both sides by 7 to eliminate the fraction:
\[ 3x < 12 \]
Divide both sides by 3:
\[ x < 4 \]
This does not yield \( x = 5 \).
**Option B: \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \)**
First, convert \( 3 \frac{2}{5} \) to an improper fraction:
\[ 3 \frac{2}{5} = \frac{17}{5} \]
The inequality becomes:
\[ \frac{3}{5}x + \frac{2}{5} > \frac{17}{5} \]
Subtract \( \frac{2}{5} \) from both sides:
\[ \frac{3}{5}x > \frac{17}{5} - \frac{2}{5} \]
\[ \frac{3}{5}x > \frac{15}{5} \]
\[ \frac{3}{5}x > 3 \]
Multiply both sides by 5 to eliminate the fraction:
\[ 3x > 15 \]
Divide both sides by 3:
\[ x > 5 \]
This does not yield \( x = 5 \).
**Option C: \( \frac{1}{5}x - \frac{3}{5} < \frac{2}{5} \)**
Add \( \frac{3}{5} \) to both sides:
\[ \frac{1}{5}x < \frac{2}{5} + \frac{3}{5} \]
\[ \frac{1}{5}x < \frac{5}{5} \]
\[ \frac{1}{5}x < 1 \]
Multiply both sides by 5 to eliminate the fraction:
\[ x < 5 \]
This does not yield \( x = 5 \).
**Option D: \( \frac{2}{5}x - \frac{4}{5} > 1 \frac{1}{5} \)**
First, convert \( 1 \frac{1}{5} \) to an improper fraction:
\[ 1 \frac{1}{5} = \frac{6}{5} \]
The inequality becomes:
\[ \frac{2}{5}x - \frac{4}{5} > \frac{6}{5} \]
Add \( \frac{4}{5} \) to both sides:
\[ \frac{2}{5}x > \frac{6}{5} + \frac{4}{5} \]
\[ \frac{2}{5}x > \frac{10}{5} \]
\[ \frac{2}{5}x > 2 \]
Multiply both sides by 5 to eliminate the fraction:
\[ 2x > 10 \]
Divide both sides by 2:
\[ x > 5 \]
This does not yield \( x = 5 \).
None of the inequalities \( x = 5 \). However, if we consider the answer choices more carefully, it's possible that there was a misinterpretation or mistake in graphing or answering. Given the conditions of the inequalities, the inequality that correctly positions \( x = 5 \) such that it fits within the graphical representation technically would be \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \) where \( x = 5 \):
Nevertheless, evaluating graphically may involve segment or dot placement analysis that matches context mathematically accurately provided positively \(x \) could affirm the options followed with a greater-than bisecting overlap on \( 5.
Use the image to answer the question.
There is a line going from -10 to 10, there is a dot on the number 5.
Hessa solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
A. 3/7x + 1/7 < 1 6/7
B. 3/5x + 2/5 > 3 2/5
C. 1/5x - 3/5 < 2/5
D. 2/5x - 4/5 > 1 1/5
3 answers
CHOOSE ONE THAT IS CLOSEST TO THE CORRECT ANSWER
Given the solutions we've worked through, the inequality that places \(x\) such that the dot would be at or near 5, considering the nature of \( x\)'s solutions involving potential overlap and directional boundaries, would be:
Option B: \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \)
This option results in \( x > 5 \), which is the closest to placing a dot at 5 when interpreted as a boundary condition. Therefore, the most reasonable answer is:
B. \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \).
Option B: \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \)
This option results in \( x > 5 \), which is the closest to placing a dot at 5 when interpreted as a boundary condition. Therefore, the most reasonable answer is:
B. \( \frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5} \).