Grade 9 Algebra L Ch. 5 Linear Inequalities

Front 1

State the Addition Property of Inequalities.

Back 1

If the same number is added to each side of a true inequality, the resulting inequality is also true.

Front 2

State the solution set {all numbers greater than or equal to 2} in 'set-builder notation',

Back 2

{x | x>= 2}

Front 3

State the Multiplication Property of Inequalities.

Back 3

1. If both sides of a true inequality are multiplied by a positive number, the resulting inequality is also true.
.
2. If both sides of a true inequality are multiplied by a negative number, the direction of the inequality sign must be reversed to make the resulting inequality also true.

Front 4

Hannah earns 100 dollars/week plus 15% commission on her sales. State a 'Multi-Step Inequality' for this problem if Hannah wants to know how much sales she needs to earn at least 250 dollars/week.

Back 4

100 + 0.15x >= 250 . where x is the dollars of sales.

Front 5

In order to ride Fire in The Hole at Silver Dollar City you must weigh at least 40 lbs (w >= 40) and at most 250 lbs (w <= 250). Write this 'Compound Inequality' as an equation without an and sign.

Back 5

40 <= w <= 250
.
The solution to this inequality is where BOTH the first AND the second inequality are true and is called the INTERSECTION of the two inequalities.

Front 6

State the inequality symbol(s) used for the following phrases: 'at most', 'no more than', and 'less than or equal to'.

Back 6

<=

Front 7

State the inequality symbol(s) used for the following phrases: 'at least', 'no less than', and 'greater than or equal to'.

Back 7

>=

Front 8

In order to ride Fire in The Hole at Silver Dollar City you must weigh at least 40 lbs (w>= 40) and at most 250 lbs (w<= 250). Write this 'Compound Inequality' as two equations in an 'or' statement for who CANNOT ride Fire in The Hole.

Back 8

w < 40 or w > 250
.only, at least, one OR the other inequality has to be true
.
The solution is called the UNION of the two inequalities.

Front 9

State the inequality signs used for the words 'within' and 'between'.

Back 9

within means >= or <=
.
between means > or <

Front 10

State the two inequalities used to solve the following absolute value inequality: | x | < 1.
Then write the solution set in set-builder notation.

Back 10

x < 1;
x > -1;
.
{x | -1 < x < 1};
Absolute value inequalities with the < sign are always AND statements; both inequalities have to be true.

Front 11

What does | x | < 1 mean in terms of the graph on a number line?

Back 11

It means the DISTANCE between x an 0 is less than 1.

Since DISTANCE is always a positive number it means that the absolute value of any linear expression, such as x, CANNOT BE A NEGATIVE NUMBER.

Front 12

What is the solution set for | x | < 0 ? (or any other negative number)

Back 12

There is no solution, The solution set is the empty set {},

Absolute value is defined as the positive value so it isn't possible for | x | to be negative.

Front 13

State the two inequalities used to solve the following absolute value inequality: | x | > 1.
Then write the solution set in set-builder notation.

Back 13

x > 1; x < -1

{x | x < -1 or x > 1};
Absolute value inequalities with the > sign are always OR statements; only, at least, one inequality has to be true.

Front 14

What is the solution set for | x | > b, where b is a negative number? for example, | x | > -3

Back 14

The solution set of all real numbers; {x | x is a real number}

Since | x | is always a non-negative number then | x | will always be greater than any negative number.

Front 15

Define what is meant by 'the graph of an inequality'.

Back 15

The graph is the set of points that represent all of the possible solutions of the inequality.
The equation with the = sign defines a BOUNDARY line that divides the coordinate plane into 2 half-planes.

Front 16

Describe when to use a SOLID line or a DASHED line to draw the BOUNDARY line.

Back 16

Use a solid line for inequalities with <= or >= signs.
Use a dashed line for inequalities with < or > signs.

Front 17

How do you decide which half-plane to shade?

Back 17

Use a test point to see which half-plane contains the points that make the inequality true and then shade that half-plane.
If the boundary line DOES NOT go through the origin then use the origin as a test point.