Chapter 1

Chapter 1:

​Equations, Expressions and Inequalities

Expressions:

Expressions are a combination of terms. (1, 3, 2x, 5w, -7m, 0)

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We simplify expressions by combining like terms.​ (2 & -5, 4x & 5x,)

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Ex: ​20x - 5y + 11x - 2 - 6y + 14

​A.

-11w + 8z - 14w - 3z - 5z

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B.

14 - 2p + 36 + 8p​

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Distribution:

​Ex:

-4(5 - 2x​)

​A.

3(-2y + 6)

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B.

12(3 + (2p - 4))​

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Cross Multiply:

We cross multiply when we have two fractions set equal to each other. ​

When we cross multiply, we multiply the terms that are diagonal from each other.

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Equations:

​Equations are similar to expressions because they both contain terms.

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Equations are unique because they contain an equal sign. (=)​

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To solve equations we use opposite operations ​to cancel out terms until we end with a solution. (x = ..., p = ..., etc.)

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Ex: 3x - 9 = 18​

Subject | Subject

Some text here about the topic of discussion

​A. B. C.

10x + 4 = -8x - 32 1/4(8x - 16) = 12

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Absolute Value Equations:

​Recall, the absolute value of a number is the positive and negative of the number.

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To solve absolute value equations we use the same steps as regular equations, but we must set the expression inside the absolute value equal to both the positive and negative number​

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Ex: |2x - 5| - 4 = 9​

Subject | Subject

Some text here about the topic of discussion

​A.

|2x + 1| = 5

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B.

|4m - 2| ​+ 9 = 11

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Inequalities

​Inequalities are like equations except instead of an equal sign, they have an inequality sign.(less than, greater than, less than or equal to,..)

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Inequalities have infinitely many solutions unlike equations who have one solution.​

Inequalities are solved the exact same as equations, with one special rule:

Ex: -2x - 5 - 3x - 5 < 0​

​A.

|y - 4| + 2 < 8

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B. -4x - 8 + 6 > 2

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​Ex: You try:​

60 < -4x - 4 < 20​ 25 < 5x - 5 < 45

Graphing Inequalities:

​To graph Inequalities we use a number line.

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We keep track of the signs of the inequality:

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We keep track of the direction of the inequality:

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Ex:

-2x - 6 > 8​

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​A. Two towns are 3.5 cm apart on a map. A key tells you 1 cm is 20 miles. How far apart are the towns in real life?

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​Writing Equations: