1. Solving Equations with Variables on both Sides.
What you’ll learn
To solve equations with variables on both sides.
To identify equations that are identities or have
no solution.
Identity: an equation that is true for every
possible value of the variable.

2. What is the solution of 5x+2=2x+14 ?
When you have variables in both sides you can use
the properties of equality and inverse operations
to write a series of simpler equivalents equations.
What is the solution of 5x+2=2x+14 ?
5x+2=2x+14
Subtract 2x from each side
-2x -2x
Simplify
3x+2=14
Subtract 2 from each side
-2 -2
Simplify.
Divide each side by 3
3x=12
3 3
Simplify
X=4
Check your answer: 5(4)+2=2(4)+14

3. Solve each equation. Check your answer.
Your turn
Solve each equation. Check your answer.
a) 3x+4=5x-10
Answer: x=7
b) 5(y-4)=7(2y+1)
Answer: Y=-3

4. + Let’s do a word problem = 1.5p=1.25p+8 You solve it
It takes a graphic designer 1.5 hours to make one page of
a web site. Using new software, the designer could complete
each page in 1.25 hours, but it takes 8 hours to learn the
software. How many Web pages would the designer have
to make in order to save time using the new software?
Design time with new software
Time to learn the software
Current design time + =
Let’s p= the number of pages the designer needs to make
1.5p=1.25p+8
You solve it
And the answer is p=32,
it will take the designer the same amount of time
To make 32 web pages using either software. The designer
Must make 33 pgs or more in order to save time using the new
Software.

5. 0.10 c+15=0.15c+10 Your turn Answer: c=100
Pristine Printing will print business cards for $0.10 each plus
a setup charge of $15. The Printing Place offers business
cards for $0.15 each with a setup charge of $10. What number
of business cards costs the same from either printer.
0.10 c+15=0.15c+10
Answer: c=100

6. Identities and Equations with no Solution
What is the solution to each equation?
Solve it by yourself
a)10x+12=2(5x+6) b) 9m-4=-3m+5+12m
10x+12=10x+12
9m-4=9m+5
-4=5
Because this is always true.
There are many solutions of
the equation. The original
equation is an identity.
Because -4=5,
The original equation has
no solution.

7. Your turn
Match each equation with the appropriate number
of solutions ?
3y-5=y+2y-9
2y+4=2(y+2)
2y-4=3y-5
Infinitely many solutions
One solution
No solution
-5=9
4=4
1=y

8. Claswork odd Homework even