Unit notes and practice questions
Everything here is for unit 4 of the Grade 9 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 9 Mathematics page. Open one at a time.
When you use it
Use when solving linear inequalities where an expression is enclosed in absolute value bars.
Watch out
Treating a greater-than absolute value inequality as a single compound inequality instead of two separate disjoint conditions.
Drafted from Grade 9 Mathematics, pages 130-161, then checked twice before it went up
When you use it
Use when finding the solution region of a linear inequality or system of linear inequalities on the coordinate plane.
Watch out
Selecting a test point that lies directly on the boundary line fails to determine which side of the region to shade.
Drafted from Grade 9 Mathematics, pages 130-161, then checked twice before it went up
| Interval | Set Inequality | Boundary Dots |
|---|---|---|
| Open dots at and | ||
| Solid dots at and | ||
| Open dot at , solid dot at | ||
| Solid dot at , open dot at |
When you use it
Use when expressing the solution set of an inequality on a number line or in interval format.
Watch out
Using square brackets or solid dots for strict inequalities includes boundary points that are not part of the solution.
Drafted from Grade 9 Mathematics, pages 130-161, then checked twice before it went up
When you use it
Use when simplifying or solving an algebraic inequality by multiplying or dividing both sides by a negative value.
Watch out
Failing to reverse the inequality direction when multiplying or dividing by a negative number changes the solution set.
Drafted from Grade 9 Mathematics, pages 130-161, then checked twice before it went up
When you use it
Use when solving factored inequalities of the form m times n greater than 0 or m times n less than 0.
Watch out
Assuming both factors have the same sign when their product is negative. They must have opposite signs.
Drafted from Grade 9 Mathematics, pages 130-161, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
According to the properties of inequalities, if a > b and m < 0, which of the following is true?
Answer: B ma < mb
Why
When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign is reversed. Since m < 0, multiplying a > b by m gives ma < mb.
Question 2
Which interval notation represents the set of all real numbers x such that -3 ≤ x < 2?
Answer: C [-3, 2)
Why
A square bracket is used for included endpoints (≤ or ≥) and a round parenthesis is used for excluded endpoints (< or >). Therefore, -3 ≤ x < 2 is written as [-3, 2).
Question 3
What is the solution set of the absolute value inequality |6x + 8| > -2?
Answer: D All real numbers
Why
The absolute value of any real number is always non-negative (greater than or equal to 0). Since 0 is always greater than -2, the inequality holds true for all real numbers.
Question 4
Solve the linear inequality 3x - 9 > 7x - 1.
Answer: B x < -2
Why
Subtract 7x from both sides: -4x - 9 > -1. Add 9 to both sides: -4x > 8. Dividing both sides by -4 reverses the inequality symbol, giving x < -2.
Question 5
What is the solution of the absolute value inequality |x + 2| < 4?
Answer: A -6 < x < 2
Why
Using the theorem for |k| < c, we write -4 < x + 2 < 4. Subtracting 2 from all parts gives -4 - 2 < x < 4 - 2, which simplifies to -6 < x < 2.
Question 6
What is the solution in interval notation for the quadratic inequality (x - 3)(x - 1) < 0?
Answer: B (1, 3)
Why
For the product of two factors to be negative, one factor must be positive and the other negative. This occurs when x - 1 > 0 and x - 3 < 0, which gives 1 < x < 3, or the interval (1, 3).
Question 7
What is the solution to the absolute value inequality |-5x - 7| ≤ 0?
Answer: D x = -7/5
Why
An absolute value cannot be strictly less than 0, so the inequality only holds when |-5x - 7| = 0. Solving -5x - 7 = 0 gives -5x = 7, so x = -7/5.
Question 8
What is the solution set of the quadratic inequality x2 - x ≥ 12?
Answer: C (-infinity, -3] U [4, infinity)
Why
Rewrite as x2 - x - 12 ≥ 0 and factor to get (x - 4)(x + 3) ≥ 0. The product is non-negative when x ≤ -3 or x ≥ 4, which is (-∞, -3] ∪ [4, ∞).
Question 9
Kebede has saved 6,000 birr for a tractor. He plans to save 1,000 birr each month until his total savings are more than 80,000 birr. If m is the number of months, which inequality and solution represent his saving plan?
Answer: A 6,000 + 1,000m > 80,000; m > 74
Why
Kebede starts with 6,000 birr and adds 1,000m birr. To have more than 80,000 birr: 6,000 + 1,000m > 80,000. Subtracting 6,000 gives 1,000m > 74,000, so m > 74.
Question 10
Chaltu has 50 birr in her phone account. She is charged 0.20 birr for each text message. If her total bill can be at most 80 birr, what is the maximum number of text messages she can send?
Answer: B 150
Why
At most means less than or equal to: 0.2m + 50 ≤ 80. Subtracting 50 gives 0.2m ≤ 30. Dividing by 0.2 gives m ≤ 150, so she can send a maximum of 150 messages.
A lesson on this chapter from YouTube. It loads only when you press play.
Compound inequalities: Linear inequalities (part 2) · Watch on YouTube
Unit 4 runs from page 130 to page 161 of the Ministry of Education edition.
Ministry of Education edition, English, 337 pages
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