To determine which inequality Hessa solved, we need to analyze the possible solutions and their graphs based on the information provided: she has a closed circle on the number 5 with an arrow pointing to the left. This indicates that the solution set includes 5 and all numbers less than 5.
Let's solve each inequality to check:
-
\( \frac{2}{5}x - \frac{4}{5} \geq 1 \frac{1}{5} \): \[ \frac{2}{5}x - \frac{4}{5} \geq \frac{6}{5} \] Adding \( \frac{4}{5} \) to both sides: \[ \frac{2}{5}x \geq \frac{6}{5} + \frac{4}{5} \implies \frac{2}{5}x \geq \frac{10}{5} = 2 \] Multiplying by \( \frac{5}{2} \): \[ x \geq 5 \] (This results in an open circle on 5 and an arrow pointing to the right.)
-
\( \frac{3}{7}x + \frac{1}{7} \leq 1 \frac{6}{7} \): \[ \frac{3}{7}x + \frac{1}{7} \leq \frac{13}{7} \] Subtracting \( \frac{1}{7} \): \[ \frac{3}{7}x \leq \frac{12}{7} \] Multiplying by \( \frac{7}{3} \): \[ x \leq 4 \] (This results in a closed circle on 4 with an arrow pointing to the left, not a match.)
-
\( \frac{1}{5}x - \frac{3}{5} \leq \frac{2}{5} \): \[ \frac{1}{5}x - \frac{3}{5} \leq \frac{2}{5} \] Adding \( \frac{3}{5} \): \[ \frac{1}{5}x \leq 1 \] Multiplying by \( 5 \): \[ x \leq 5 \] (This results in a closed circle on 5 with an arrow pointing to the left, which is a match.)
-
\( \frac{3}{5}x + \frac{2}{5} \geq 3 \frac{2}{5} \): \[ \frac{3}{5}x + \frac{2}{5} \geq \frac{17}{5} \] Subtracting \( \frac{2}{5} \): \[ \frac{3}{5}x \geq 3 \] Multiplying by \( \frac{5}{3} \): \[ x \geq 5 \] (This results in an open circle on 5 and an arrow pointing to the right.)
Based on the analysis, the correct inequality that Hessa solved is:
\( \frac{1}{5}x - \frac{3}{5} \leq \frac{2}{5} \).
0 answers