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Expressions and Equations

 

 

 Vocabulary Poster

 

 Click Here for a Review Sheet of this unit on Expressions & Equations

  Unit Review Sheet with vocabulary and examples.docx  

 

In 7th grade students solve:

 

equations of the form "ax + b = c" and "a(x + b) = c".

inequalities of the form "ax + b > c", "ax + b < c",

                              "ax + b ≤ c", and "ax + b ≥ c".

 

Students solve one-step equations in 6th grade. They should know that solving an equation means to find the number that will replace the variable and make the equation "true".

 

Here are some notes to help with solving equations and inequalities:

 

  Class Notes:  Expressions vs Equations Notes & Examples.ppt  

 

 

In order to solve an equation the variable must be on one side of the equation by itself. We isolate the variable. Then the value that is on the other side of the equation is the solution.

Check answers by replacing the variable with the solution in the original equation. Both sides of the equation should have the same value. If they do not have the same value, the solution is incorrect.

 

Equation Examples

 

Example 1:

 

3y+4=10 Original Equation

 

 

3y+4-4=10-4 Undo addition or subtraction by inverse operations

 

 

3y=6 Simplify

 

 

3y = 6 Divide by the coefficient of y (Could multiply by the reciprocal of the coefficient) 

3     3

 

 

y=2

 

Check: 3(2)+ 4=10

         6+4=10

         10=10

 

Example 2:

 

-2 (w+3)=12 Original Equation


-2 (w) + (-2)(3)=12 Apply distributive property


-2w + (-6)=12 Simplify


-2w + (-6) + 6 = 12 + 6 Add the inverse of -6


-2w = 18 Simplify


-2w = 18
-2      -2  Undo multiplication by dividing


w = -9

 

Check: -2(-9 +3)=12

           -2(-6)=12

           12=12

 

In order to graph the solution of an equation we mark the number on a number line.

 

 

Inequalities are solved using the same basic steps. There are two basic differences.

  •  An inequality has a boundary point and an infinite number of solutions. The graph will show the boundary point and part of the number line shaded to represent the other solutions.
  •  The inequality symbol must be reversed when multiplication or division by a negative number is required to isolate the variable.

 

Inequality Example

 

3x - 4 < -7


3x - 4 + 4 < -7 + 4


3x < -3
3       3

x < -1  The inequality symbol did not change because we divided by a positive 3.


The open circle means that -1 is not a solution, but any number less than -1 is a solution.

 

 Inequality Graph

 

 

Why does the inequality symbol change when we multiply or divide by a negative number?

 

Take a true inequality. 10 > 4

 

Add a positive number to both sides. 10+2>4+2           12>6 Still true.

 

Add a negative number to both sides. 10+(-2)>4+(-2)     8>2 True.

 

Multiply by a positive number. 10(2)>4(2)                      20>8 True.

 

Multiply by a negative number. 10(-2)>4(-2 )                 -20>-8 False.  

                                                                                 -20True.

 

Divide by a positive number.     10 › 4                             5>2 True.

                                           2    2

 

Divide by a negative number.    10 › 4                        –5>–2 False.     

                                          -2   -2                        –5<–2 True. 

Make the false inequalities true by reversing the inequality symbol.

 

 

Inequality

Symbols

Can you remember the name of the symbol?

1. ≤            a. less than

2. ≥            b. greater than

3. ˂            c. less than or equal to

4. ˃            d. greater than or equal to

Answers:

1. c  2. d  3. a  4. b

 

 Want to test your knowledge or get some extra practice?  Check out these weblinks below!

 

CCSS.Math.Content.7.EE Expressions and Equations