Question

1. consider the inequality -\frac{1}{10}x + 1\frac{2}{5} \geq 1\frac{7}{10}.

part a
solve the inequality -\frac{1}{10}x + 1\frac{2}{5} \geq 1\frac{7}{10}.
complete the sentence to describe how to graph the solution on a number line.
the solution can be graphed by plotting an open circle, a closed circle at the number -3, 3 and shading the number line to the left, right of the circle.
part b
select all the values of x that are solutions for this inequality.
-8, -6, -3, 0, 3, 6

Explanation:

Step1: Convert mixed numbers to improper fractions

\(-\frac{1}{10}x + 1\frac{2}{5}\geq1\frac{7}{10}\) becomes \(-\frac{1}{10}x+\frac{7}{5}\geq\frac{17}{10}\)

Step2: Subtract \(\frac{7}{5}\) from both sides

\(-\frac{1}{10}x+\frac{7}{5}-\frac{7}{5}\geq\frac{17}{10}-\frac{7}{5}\)
\(-\frac{1}{10}x\geq\frac{17 - 14}{10}\)
\(-\frac{1}{10}x\geq\frac{3}{10}\)

Step3: Multiply both sides by \(- 10\) (and reverse the inequality sign)

\(x\leq - 3\)

Answer:

Part A:

• A closed circle (because the inequality is \(\leq\), which includes the endpoint)
• At the number \(-3\)
• Shading to the left (since \(x\leq - 3\))

Part B:

• \(-8\) (because \(-8\leq - 3\))
• \(-6\) (because \(-6\leq - 3\))
• \(-3\) (because \(-3=-3\))