Download 1.1 Solving Simple Equations - Liberty Union High School District

Warm Up
HW check
Each cylinder is equivalent to two blocks.
The balance problem is equivalent to x + 5 = 3x + 1,
where a cylinder represents x and the cubes
represent the whole numbers. This is an example of
an equation with variables on both sides, the type
you will solve today.
Exploration #1- work with your
seat partner
If you finish before time is up…keep going!
1.3 Solving Equations with
Variables on Both Sides
Today’s Learning Goal is: Students
will be able to solve linear equations,
identify special solutions and use
linear equations to solve real-life
problems.
To solve an equation with variables on both
sides, simplify one or both sides of the
equation, then use inverse operations to
collect the variable terms on one side,
constant terms on the other and then isolate
the variable.
Examples
1. 10 – 4x = -9x
10 -4x + 4x = -9x + 4x
10 = -5x
10=-5x
-5 -5
-2 = x
Add 4x to both sides
Combine Like Terms
Divide both sides by -5
Examples
2. 3(3x – 4) = ¼ (32x + 56)
9x – 12 = 8x + 14
9x-12+12 = 8x +14 +12
9x = 8x +26
9x – 8x = 8x – 8x + 26
x = 26
Distribute the 3 and the 1/4
Add 12 to both sides
Combine Like Terms
Subtract 8x from both sides
Combine Like Terms
You try
1. -2x = 3x + 10
x = -2
2. ½ (6h – 4) = -5h + 1
h = 3/8
3. - ¾ (8n + 12) = 3 (n – 3)
n=0
Special Solutions of Linear Equations
Equations do not always have one solution. An
equation that is true for all values of the
variable is an identity and has infinitely many
solutions. An equation that is not true for any
value of the variable has no solution.
Examples
Identify the Number of Solutions
3. 3(5x + 2) = 15x
15x + 6 = 15x
-15x
-15x
This is never true so
6≠0
the equation has no
solution
Examples
Identify the Number of Solutions
4. -2 (4y + 1) = -8y – 2
-8y - 2 = -8y – 2
+8y
+8y
-2 = -2
This is always true, so
the equation is an identity
and has infinitely many
solutions.
You Try!
4. 4(1 – p) = -4p + 4
Infinite solutions
5. 6m – m = 5/6 (6m – 10)
No solution
6. 10k +7 = -3 – 10k
k=-
1
2
7. 3 (2a – 2) = 2 (3a – 3)
Infinite solutions
Video
• https://www.bigideasmath.com/protected/co
ntent/stem/video.php?id=100828676
Examples
Modeling with Mathematics
4. A boat leaves New Orleans and travels
upstream on the Mississippi River for 4 hours.
The return trip takes only 2.8 hours because
the boat travels 3 miles per hour faster
downstream due to the current. How far does
the boat travel upstream?
Examples
- Understand the Problem
You are given the amounts of time the boat
travels and the difference in speeds for each
direction. You are asked to find the distance the boat
travels.
- Make a Plan
Use the Distance Formula (distance = rate * time)
to write expressions that represent the problem.
Examples
- Solve the Problem
distance upstream = rate * time
distance downstream = rate * time
rate * time = rate * time
Is the
answer
reasonable?
You Try!
17.5 mi
Workbook p. 15 & 16 with your
seat partner
*each student does and shows the work in their
own workbook – your partners are there to help
you!