Download Unit 3 Help for Parents

Unit 3 Algebra
How do you write variable expressions and equations?
expression – a math phrase with no equal sign
equation – a math sentence with an equal sign
ex: 2 + 3
ex: 2 + 3 = 5
4x – 16
4x – 16 = 32
To write phrases or sentences as expressions and equations, look for key words that tell you whether to add, subtract,
multiply, or divide. You can use a variable (letter) to represent a number that you do not know. The word “is” tells you
where the equal sign should go.
ex: 3 more than a number  x + 3
The quotient of a number and 6 is 8  x ÷ 6 = 8
Practice website:
Writing expressions - http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-game.html
Simplifying Expressions: In an expression, the parts are called terms. When terms use the same variable, they are called
like terms. A term that has no variable is called a constant. To simplify an expression, you combine all constants. You
also combine all like terms.
Ex: x + 5 + 3x + 2  You can combine x and 3x because they use the same variable  x + 3x = 4x
 You can combine 5 + 2 because they are both constants  5 + 2 = 7
x + 5 + 3x + 2  4x + 7
Evaluating Expressions: To evaluate an expression, substitute a number for each variable and then solve the
expression.
Ex: Evaluate 4 + t for t = 7  4 + 7  11
Evaluate 13 – r when r = 3  13 – 3  10
How do you solve one-step equations?
To solve an equation, use inverse (opposite) operations. Do the same thing to both sides of the equal sign to get the
variable by itself on one side.
Ex: y + 25 = 40
n - 6 = 14
5 x = 20
x/7 = 3
- 25 - 25
+6 + 6
5
5
·7 ·7
0
15
0
20
x=4
21
y = 15
n = 20
x = 21
Practice Website:
Solving Equations - http://www.math-play.com/soccer-math-one-step-equations-game/one-step-equations-game.html
How do you write and solve inequalities?
inequality – a statement formed by placing an inequality symbol between two expressions
Symbols: > = is greater than < = is less than ≤ = is less than or equal to ≥ = is greater than or equal to
You solve an inequality by finding a solution. The solution is the set of all numbers that make the statement true. Solve
the inequality the same way you solve an equation. The graph of an inequality is all the points on a number line that
represent the solution. An open dot means that number is NOT part of the solution. (used with < or >) A closed dot
means that number IS part of the solution. (used with ≥ or ≤)
Unit 3 Algebra
Example: Solve the inequality x + 2 ≥ 3.
Solve like an equation by subtracting
2 from each side so the x is by itself.
pointing to the right.
solution of the inequality.
x + 2 ≥ 3
-2 -2
1
Since the solution uses ≥, the graph
graph will use a closed dot, starting
at 1 and
Then write the
x≥1
How do you evaluate functions and write function rules?
function – a pairing of each number in one set with a number in a second set
- the numbers that you start with are called input. They represent the x value. This is called the independent
value because it is usually given.
- the numbers that you pair with the input are called the output. They represent the y value. This value is the
dependent value because it depends on the input value.
To solve functions, you can make an input-output table.
ex: y = x + 5
x
1
3
5
So:
y
substitute the number
for the x to solve for
the y value
y=x+5
x
1
3
5
y
6
8
10