Transcript Solving One Step Equations. - Math GR. 6-8

(8x – 1)2 + y
Objectives:
1. To be able to recognize the
difference between an expression
and an equation.
2. To be able to solve one step
equations using a physical model.
Expression or Equation?
Solving One-Step
Equations
Definitions
Term: a number, variable or the
product or quotient of a number
and a variable.
examples:
12
z
2w
c
6
Terms are separated by addition (+)
or subtraction (-) signs.
3a – ¾b + 7x – 4z + 52
How many Terms do you see?
5
Definitions
Constant: a term that is a number.
Coefficient: the number value in
front of a variable in a term.
3x – 6y + 18 = 0
What are the coefficients? 3 , 6
What is the constant?
18
Solving One-Step Equations
A one-step equation means you only have to
perform 1 mathematical operation to solve it.
You can add, subtract, multiply or divide to
solve a one-step equation.
The object is to have the variable by itself on
one side of the equation.
Solving One Step Equations
involving adding and
subtracting.
x + 7 = -13
- 7
- 7
x = -20
What do need to do to both sides
of the equation to get the variable
by itself?
What happens to the left side of
the equation?
What happens to the right side of
the equation?
What is the solution of the
equation?
Solving One Step Equations.
What would the previous equation look like if we
used physical models to express it?
x + 7 = -13
x
Solving One Step Equations.
What would the following equation look like if we
used physical models to express it?
-5 = y - 12
y
Solving One Step Equations.
What would the following equation look like if we
used physical models to express it?
14 = a - 9
a
Example 1: Solving an addition equation
t + 7 = 21
To eliminate the 7 add its opposite to both sides of the
equation.
t + 7 = 21
t + 7 -7 = 21 - 7
t + 0 = 21 - 7
t = 14
Example 2:
Solving a subtraction equation
x – 6 = 40
To eliminate the 6 add its opposite to
both sides of the equation.
x – 6 = 40
x – 6 + 6 = 40 + 6
x = 46
Example 3:
Solving a multiplication equation
8n = 32
To eliminate the 8 divide both sides of the
equation by 8. Here we “undo” multiplication
by doing the opposite – division.
8n = 32
8
8
n=4
Example 4:
Solving a division equation
x
 11
9
To eliminate the 9 multiply both sides of the
equation by 9. Here we “undo” division by doing
the opposite – multiplication.


x
 11
9
x
9  (11)(9)
9

x  99
What are Inequalities?
Inequality Signs
Definition
Sig
n
>
Greater Than
<
Less Than
≥
Greater Than or Equal to
≤
Less Than or Equal to
≠
Not Equal to
Just remember
• We read inequalities just like we read
books, from left to right.
• Lets see how we read the following:
6> 2
6 is greater than 2
• You need to remember which sign it is.
– Just as which would Pacman rather eat?
– The bigger number!
What does an open dot mean?
3.5
3.99
3.9
The value 4 is not
included
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
The value 4 is included
What does an open dot mean?
Sign
Dot
Open dot
<
≤
Si
Closed dot
>
Open dot
≥
Closed dot
Inequalities
• Inequalities are similar to
equations when solving. You
can add, subtract, multiply or
divide any amount to either
side as long as you do it to
both sides.
Graphing 1-variable Inequalities
Steps
1. Read the inequality and identify the sign.
2. Draw a number line using the number from the
inequality as the central number.
3. Label numbers to either side of it.
4. Place the appropriate dot on the number line on
the central number.
5. Draw an arrow in the appropriate direction.
(choose a number from the number line and test
it in the inequality)
Example:
Graph the inequality: x < 10
X is less than 10
6
7
8
9
10 11
12
13 14
•The point for 10 in not included, so The circle is
open.
•Now pick a point other then 10 and test it
-Lets try 11 so 11<10 is not true so the arrow
goes the other way
Solve x - 6 < 10 and graph the solution.
x  6  10
x  6 +6  10 +6
x  16
The point 16 in not included. The circle is open.

12
13
14
15
16
17
18
19
20
Solve y  8  15 and graph the solution.

y  8  15
y  8 -8 15 -8
y7
4
5
6
7
8
9
10
11
12
Write an inequality for the graph.
2
3
4
5
6
7
8
9
10
Closed dot means the number 4 is included.
x 4
Solve 9 x  36 and graph the solution on a number line.
9x  36
9
 36
x
9
9
x  4
-6
-5
-4
-3
-2
-1
0
1
2
BACK
Solve - 4x  12 and graph the solution on a number line.
9x  36
9x  36
-4
Since
= 1 we can
-4
say 1x on the left.
x 4
Also since 1x = x
we have just x on the left



0
1
9
9
2
3
4
5
6
7
8
Solve - 4x  12 and graph the solution on a number line.
 4 x  12
 4 x  12
-4 -4
-4
Since
= 1 we can
-4
say 1x on the left.
Also since 1x = x
we have just x on the left
x  3
When you multiply/divide both
sides by a negative flip the sign

-6
-5

-4
-3
-2
-1
0
1
2
x
Solve  42 and graph the solution on a number line.
6
6
Since = 1 we can
6
say 1x on the left.

Also since 1x = x
we have just x on the left
x
 42
6
x
(6)  42 (6)
6
x 7

4
5

6
7
8
9
10
11
12
When you multiply or
divide each side of an
inequality by a negative
integer, you must reverse
the order symbol.
Do you change the sign
if you multiply or divide
by a positive number
while solving?
NO!!!!
Do you change the sign?
15  5a No
y
 20
4
No
 3m  33 Yes
BACK