Question 1

Which of the following is the correct interval notation for the solution set of $$x \u003c 5$$?

Accepted Answer

$$(-\infty, 5)$$

Question 2

Solve the inequality $$19 + 7x \geq 2x - 5. $$Write the solution set using interval notation.

Accepted Answer

$$[ -4, \infty )$$

Question 3

Which of the following inequalities is represented by the interval notation $$(a, \infty)$$?

Accepted Answer

$$x \u003e a$$

Question 4

Solve the inequality $$7(x - 3) \u003c 2(4x - 1). $$Write the solution set in interval notation.

Accepted Answer

$$(-\infty, 5.5)$$

Question 5

Solve the inequality $$-3(x - 1) \u003c -2[5 + 8(x + 5)]. $$Write the solution set in interval notation.

Accepted Answer

$$(-\infty, 2)$$

Question 6

Solve the inequality $$\frac{1}{2} + \frac{3}{7} \geq \frac{x}{14}. $$Write the solution set in interval notation.

Accepted Answer

$$(-\infty, 11]$$

Question 7

Solve the inequality $$3(x - 6) + 3x - 10 \geq 2(x - 8) + 10x. $$Write the solution set using interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 8

Solve the inequality $$4x + 1 \u003c 4(x - 2). $$Write the solution set in interval notation.

Accepted Answer

$$(-\infty, -2)$$

Question 9

A chemical process requires the temperature $$T to be at $$least $$80$$ degrees but less than $$120$$ degrees. Which interval notation correctly represents the acceptable temperature range?

Accepted Answer

$$[80, 120)$$

Question 10

If $$x$$ must satisfy $$x \leq 7$$, which of the following is the correct interval notation?

Accepted Answer

$$(-\infty, 7]$$

Question 11

A medication is effective only if the dosage $$d (in mg) $$satisfies $$d \u003e 50. $$Which of the following is the correct interval notation for the effective dosage?

Accepted Answer

$$(50, \infty)$$

Question 12

Which of the following is the correct solution set for $$x \geq -3$$?

Accepted Answer

$$[-3, \infty)$$

Step-by-Step Guidance for Solving Linear Inequalities and Expressing Solutions in Interval Notation

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