Flashcards · 9 cards

Inequalities

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Know it
Solving an inequality: what is the one rule that differs from an equation?
Answer
Multiplying or dividing by a negative number turns the sign round: $-2x > 6$ gives $x < -3$ .
From the lesson: Solving linear inequalities
Rule
On a number line, what do a filled circle and an open circle mean?
Answer
Filled: the end is included ( $\le$ or $\ge$ ). Open: it is not ( $<$ or $>$ ).
x ≤ 3Filled circle: 3 is included
From the lesson: Solving linear inequalities
Rule
How do you show $-1 \le x < 4$ on a number line?
Answer
Between −1 and 4, with a filled circle at −1 (included) and an open circle at 4 (not included).
−1 ≤ x < 4Between −1 and 4: −1 in, 4 out
From the lesson: Solving linear inequalities
Know it
How do you clear fractions from an inequality?
Answer
Multiply every term by the LCM, including terms with no fraction. The LCM is positive, so the sign stays the same.
From the lesson: Solving linear inequalities
Rule
What does $|x - a| < b$ mean?
Answer
$a - b < x < a + b$ : $x$ is within $b$ of $a$ . So $|x - 1| < 4$ gives $-3 < x < 5$ .
|x − 1| < 4Within 4 of 1: −3 < x < 5
From the lesson: Solving linear inequalities
Rule
How do you show $y \le \frac12 x + 1$ on a graph?
Answer
Draw the line $y = \frac12 x + 1$ : solid for $\le$ , broken for $<$ . Test a point not on the line, such as $(0, 0)$ , and shade the side where the inequality is true.
y ≤ ½x + 1Solid line: points on the line count. Shade below.
From the lesson: Inequalities on a graph
Know it
Which point do you test to find the right side of a line?
Answer
Any point not on the line. $(0, 0)$ is easiest; if the line passes through the origin, use $(1, 0)$ or $(0, 1)$ .
From the lesson: Inequalities on a graph
Know it
How do you solve $x^2 + 4x - 21 < 0$ ?
Answer
Find where it equals 0: $(x + 7)(x - 3) = 0$ gives $-7$ and $3$ . The answer is a range: here between them, $-7 < x < 3$ .
From the lesson: Inequalities on a graph
Which method?
WAEC 2019 · Paper 2 · Q1 (a)
Solve the inequality $\dfrac{1 + 4x}{2} - \dfrac{5 + 2x}{7} < x - 2$ .
What is the first step?
Answer
Multiply every term by 14, the LCM of 2 and 7, including the $x - 2$ on the right.
From the lesson: Solving linear inequalities Try the question