Question

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How is an inequality different from an equation?
What are four ways inequality can be written?
What would the graph of each inequality look like on a number line? (use an example)
What would the graph of an equation look like on a number line(use an example)


Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and a balance scale.

Explain the Golden Rule for solving equations
using an example.


What does it mean if a situation has a condition or constraint? Give an example.


Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.

Answer 1

An inequality is different from an equation because it uses inequality symbols to show a comparison between expressions. Examples of four ways an inequality can be written are given, along with an explanation of their graph on a number line. The graph of equations on a number line is also described, with examples provided.

Step-by-step explanation:

An inequality is different from an equation because:

1. An inequality uses inequality symbols (such as <, >, ≤, ≥) to compare two expressions that are not necessarily equal, while an equation uses an equal sign (=) to show that two expressions are equal.
2. An inequality has an infinite number of solutions, while an equation typically has a finite number of solutions.
3. An inequality represents a range of possible values, while an equation represents a specific value.

Four ways an inequality can be written are:

1. x < 5 (less than)
2. y ≥ 3 (greater than or equal to)
3. z > -2 (greater than)
4. w ≤ 7 (less than or equal to)

The graph of each inequality on a number line:

• The graph of x < 5 would be an open circle on 5 and an arrow pointing to the left.
• The graph of y ≥ 3 would be a closed circle on 3 and an arrow pointing to the right.
• The graph of z > -2 would be an open circle on -2 and an arrow pointing to the right.
• The graph of w ≤ 7 would be a closed circle on 7 and an arrow pointing to the left.

The graph of an equation on a number line:

• The graph of x = 4 would be a closed circle on 4.
• The graph of y = -2 would be a closed circle on -2.
• The graph of z = 0 would be a closed circle on 0.
• The graph of w = 8 would be a closed circle on 8.