Question 1

Solve the inequality $$\frac{5}{6}x \geq -7$$ and express the solution in interval notation.

Accepted Answer

$$[-\frac{42}{5}, \infty)$$

Question 2

Which property of inequalities allows you to multiply both sides of $$\frac{5}{6}x \geq -7 by$$ $$\frac{6}{5}$$ without reversing the inequality sign?

Accepted Answer

Multiplication by a positive number

Question 3

What is the value of $$x$$ that forms the endpoint of the solution set for $$\frac{5}{6}x \geq -7$$?

Accepted Answer

$$-\frac{42}{5}$$

Question 4

When graphing the solution to $$\frac{5}{6}x \geq -7$$, which symbol should be used at the endpoint $$x = -\frac{42}{5}$$?

Accepted Answer

A bracket

Question 5

If the inequality was $$\frac{5}{6}x \u003e -7$$ instead, what would the interval notation for the solution be?

Accepted Answer

$$(-\frac{42}{5}, \infty)$$

Question 6

A chemical process requires the temperature $$T (in$$ $$^\circC) to $$satisfy $$\frac{5}{6}T \geq -7. $$What is the minimum temperature allowed for the process?

Accepted Answer

$$T = -\frac{42}{5}$$

Question 7

Which of the following values is a solution to $$\frac{5}{6}x \geq -7$$?

Accepted Answer

$$x = -8.4$$

Question 8

If $$x$$ represents the number of hours a machine operates and must satisfy $$\frac{5}{6}x \geq -7$$, what is the least number of hours the machine can operate?

Accepted Answer

$$-8.4$$ hours

Question 9

Which of the following best describes the solution set for $$\frac{5}{6}x \geq -7$$?

Accepted Answer

All real numbers greater than or equal to $$-\frac{42}{5}$$

Question 10

If the inequality was $$\frac{5}{6}x \leq -7$$, what would the solution in interval notation be?

Accepted Answer

$$(-\infty, -\frac{42}{5}]$$

Question 11

A medical dosage $$d$$ must satisfy $$\frac{5}{6}d \geq -7 to be $$safe. Which of the following dosages is NOT safe?

Accepted Answer

$$d = -9$$

Question 12

Which step is necessary to isolate $$x in $$the inequality $$\frac{5}{6}x \geq -7$$?

Accepted Answer

Multiply both sides by $$\frac{6}{5}$$

Question 13

If $$x$$ must satisfy $$\frac{5}{6}x \geq -7$$ for a financial investment to be profitable, what is the minimum value of $$x$$ for profitability?

Accepted Answer

$$x = -\frac{42}{5}$$

Question 14

Which of the following is the correct graph representation for the solution to $$\frac{5}{6}x \geq -7$$?

Accepted Answer

A number line shaded to the right of $$-\frac{42}{5}$$ with a bracket at $$-\frac{42}{5}$$

Solving Linear Inequalities and Expressing Solutions in Interval Notation

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