True or False? You can add or subtract terms to both sides of a linear inequality in exactly the same way as you do to a linear equation.

True. You can add or subtract terms to both sides of a linear inequality in exactly the same way as you do to a linear equation.

True or False? You can multiply or dividing both sides of a linear inequality in exactly the same way as you do to a linear equation.

False. You can multiply or dividing both sides of a linear inequality in exactly the same way as you do to a linear equation as long as you multiply or divide by positive numbers. If, however, you multiply or divide both sides by negative numbers, you have to flip the direction of the inequality sign.

IGCSEMaths A: HigherEdexcelFlashcards

Solving Inequalities (Edexcel IGCSE Maths A)

Flashcards

1/15

FrontSolving Linear Inequalities
Define the word inequality in algebra.
FrontSolving Linear Inequalities
Explain the meaning of the word linear in linear inequality.
BackSolving Linear Inequalities
The word linear in linear inequality means that the terms in the inequality are either constant numbers or terms in $x$ , but not terms in $x^{2}$ or $x^{3}$ etc.
These are examples of linear inequalities:
$x + 2 > 5$
$2 x < x - 1$

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Cards in this collection (15)

Define the word inequality in algebra.
An inequality compares a left-hand side to a right-hand side and states which one is bigger, using the symbols $<, >, \leq, \geq$ .
Explain the meaning of the word linear in linear inequality.
The word linear in linear inequality means that the terms in the inequality are either constant numbers or terms in $x$ , but not terms in $x^{2}$ or $x^{3}$ etc.
These are examples of linear inequalities:
- $x + 2 > 5$
- $2 x < x - 1$
True or False?
You can add or subtract terms to both sides of a linear inequality in exactly the same way as you do to a linear equation.
True.
You can add or subtract terms to both sides of a linear inequality in exactly the same way as you do to a linear equation.
True or False?
You can multiply or dividing both sides of a linear inequality in exactly the same way as you do to a linear equation.
False.
You can multiply or dividing both sides of a linear inequality in exactly the same way as you do to a linear equation as long as you multiply or divide by positive numbers.
If, however, you multiply or divide both sides by negative numbers, you have to flip the direction of the inequality sign.
How do number lines highlight the difference between strict inequalities (such as $x > 2$ ) and non-strict inequalities (such as $x \geq 2$ )?
Number lines show an open circle for strict inequalities (such as $x > 2$ ) and a closed circle for non-strict inequalities (such as $x \geq 2$ ).
True or False?
The number line representing " $x < 1$ or $x > 3$ " consists of two separate arrows pointing outwards in opposite directions.
True.
The number line representing " $x < 1$ or $x > 3$ " consists of two separate arrows pointing outwards in opposite directions.
True or False?
The inequality $\{x : x \leq 10\} \cup \{x : x \geq 20\}$ is the same as $10 \leq x \leq 20$ .
False.
The inequality $\{x : x \leq 10\} \cup \{x : x \geq 20\}$ is not the same as $10 \leq x \leq 20$ .
The $\cup$ means 'or' so the answer is $x \leq 10$ or $x \geq 20$ .
Explain how to find the number of integer values of $x$ that lie in the range $\{x : x > 1\} \cap \{x : x < 5\}$ .
To find the number of integer values of $x$ that lie in the range $\{x : x > 1\} \cap \{x : x < 5\}$
1. Interpret the set notation as $1 < x < 5$
2. Check if the inequalities are strict (both are)
3. This means that only the integers 2, 3 and 4 are accepted
So there are three integers that lie in that range.
Explain how you would solve an inequality in the form $- 10 < a x + b < 10$ .
To solve an inequality in the form $- 10 < a x + b < 10$ ,
1. Subtract $b$ from all three parts to get $- 10 - b < a x < 10 - b$
2. Then divide all three parts by $a$ to get $\frac{- 10 - b}{a} < x < \frac{10 - b}{a}$
An alternative method is to split into two different inequalities, $- 10 < a x + b$ and $a x + b < 10$ , then solve these individually.
Define a quadratic inequality.
A quadratic inequality is an inequality involving terms in $x^{2}$ . They have the form $a x^{2} + b x + c > 0$ , or $< 0$ , or $\geq 0$ or $\leq 0$ .
How do you solve a quadratic inequality in the form $(x - a) (x - b) < 0$ , where $a < b$ ?
To solve a quadratic inequality in the form $(x - a) (x - b) < 0$ , where $a < b$ :
1. Find the roots of $(x - a) (x - b) = 0$ which are $a$ and $b$
2. Sketch the graph of $y = (x - a) (x - b)$ which is a positive U-shape through $a$ and $b$ on the $x$ -axis
3. Check if you want the parts of the curve above the $x$ -axis ( $> 0$ ) or below the $x$ -axis ( $< 0$ ). This one is below, ( $< 0$ )
4. Write the range of $x$ values on the $x$ -axis that span this region
The answer is $a < x < b$ .
How do you solve a quadratic inequality in the form $(x - a) (x - b) \geq 0$ , where $a < b$ ?
To solve a quadratic inequality in the form $(x - a) (x - b) \geq 0$ , where $a < b$
1. Find the roots of $(x - a) (x - b) = 0$ which are $a$ and $b$
2. Sketch the graph of $y = (x - a) (x - b)$ which is a positive U-shape through $a$ and $b$ on the $x$ -axis
3. Check if you want the parts of the curve above the $x$ -axis ( $\geq 0$ ) or below the $x$ -axis ( $\leq 0$ ). This one is above, ( $\geq 0$ )
4. Write the range of $x$ values on the $x$ -axis that span these two different regions
The answer is $x \leq a$ or $x \geq b$ .
True or False?
The solution $x < - 3$ or $x > 6$ can be written more simply as $6 < x < - 3$ .
False.
The solution $x < - 3$ or $x > 6$ can not be written more simply as $6 < x < - 3$ .
That is because no number is bigger than 6 but less than -3. This means the answer $x < - 3$ or $x > 6$ is already written in its simplest form.
True or False?
Solving $x^{2} < 9$ gives $x < 3$ .
False.
Solving $x^{2} < 9$ does not gives $x < 3$ .
You need to bring terms to the positive $x^{2}$ side ( $x^{2} - 9 < 0$ ) then factorise, giving $(x + 3) (x - 3) < 0$ . The roots are $- 3$ and $3$ .
For the curve $y = (x + 3) (x - 3)$ , the region below ( $<$ ) the $x$ -axis is $- 3 < x < 3$ , which is the correct answer.
True or False?
An inequality with a negative $x^{2}$ term can always be rewritten as an inequality with a positive $x^{2}$ term.
True.
An inequality with a negative $x^{2}$ term can always be rewritten as an inequality with a positive $x^{2}$ term.
For example, $- x^{2} + x + 6 < 0$ can be rewritten as $0 < x^{2} - x - 6$ by adding terms to the other side, which gives $x^{2} - x - 6 > 0$ .
Alternatively you can multiply both sides by $- 1$ , but this will change the sign of the inequality as you are multiplying by a negative: $x^{2} - x - 6 > 0$

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