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 .

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Solving Inequalities (AQA GCSE Maths)

Flashcards

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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 divide both sides of a linear inequality in exactly the same way as you do to a linear equation.
False.
You can multiply or divide 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.
E.g. you can divide $\begin{array}{rcl} 2 x & < & 4 \end{array}$ by 2 to get $\begin{array}{rcl} x & < & 2 \end{array}$ .
You can divide $\begin{array}{rcl} - 2 x & < & 4 \end{array}$ by -2, but you must flip the inequality to get $\begin{array}{rcl} x & > & - 2 \end{array}$ .
How do number lines highlight the difference between strict inequalities (such as $x < 3$ ) and non-strict inequalities (such as $x \leq 3$ )?
Number lines show an open circle for strict inequalities, e.g. $x < 3$ , and a closed circle for non-strict inequalities, e.g. $x \leq 3$ .
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 diagram below shows the inequality $- 4 < x \leq 2$ .
False.
The number line in the diagram does not show the inequality $- 4 < x \leq 2$ .
It has two open circles which indicate the inequality $- 4 < x < 2$ .
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.
2. Then divide all three parts by $a$ .
E.g. $- 10 < 2 x + 6 < 10 - 16 < 2 x < 16 - 8 < x < 8$
(Though if $a$ is negative, remember to 'flip' the inequality signs when dividing.)
An alternative method is to split into two different inequalities, $- 10 < 2 x + 6$ and $2 x + 6 < 10$ , then solve these individually.
How would " $x$ is greater than or equal to 3" be written using set notation?
" $x$ is greater than or equal to 3" would be written using set notation as:
$\{x : x \geq 3\}$
How would " $x$ is greater than 3 and less than 6" be written using set notation?
" $x$ is greater than 3 and less than 6" would be written using set notation as:
$\{x : x > 3\} \cap \{x : x < 6\}$ or $\{x : 3 < x < 6\}$
How would " $x$ is less than 2 or greater than 8" be written using set notation?
" $x$ is less than 2 or greater than 8" would be written using set notation as:
$\{x : x < 2\} \cup \{x : x > 8\}$
Outline how to solve a quadratic inequality, such as $a x^{2} + b x + c > 0$ .
To solve a quadratic inequality such as $a x^{2} + b x + c > 0$ :
- Find the roots of the quadratic equation $a x^{2} + b x + c = 0$ .
- Sketch a graph of the quadratic and label the roots.
  If it is a positive quadratic it will be U-shaped.
  If it is a negative quadratic it will be n-shaped.
- Identify the region that satisfies the inequality.
  For $a x^{2} + b x + c > 0$ the region above the x-axis satisfies the inequality.
The graph of $y = x^{2} - 7 x + 10$ is shown below.
Use the graph to find the answer to $x^{2} - 7 x + 10 > 0$ .
Shade the region which satisfies $x^{2} - 7 x + 10 > 0$ (above the x-axis).
The answer is $x > 5$ or $x < 2$ .
The graph of $y = x^{2} - 2 x - 15$ is shown below.
Use the graph to find the answer to $x^{2} - 2 x - 15 < 0$ .
Shade the region which satisfies $x^{2} - 2 x - 15 < 0$ (below the x-axis).
The answer is $- 3 < x < 5$ .
The graph of $y = - x^{2} + 4 x + 12$ is shown below.
Use the graph to find the answer to $- x^{2} + 4 x + 12 > 0$ .
Shade the region which satisfies $- x^{2} + 4 x + 12 > 0$ (above the x-axis).
The answer is $- 2 < x < 6$ .

1. Number

2. Algebra

3. Ratio, Proportion & Rates of Change

4. Geometry & Measures

5. Probability

6. Statistics