2.4 Solving Equations with Variables on Both Sides: Identity: an equation that has infinitely many solutions. Infinitely Many Solutions: An equation that is true for any and every possible value. No Solution: an equation has no solution if there is no value to make the equation TRUE.
25
Embed
2.4 Solving Equations with Variables on Both Sides: Identity: an equation that has infinitely many solutions. Infinitely Many Solutions: An equation that.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
2.4 Solving Equations with Variables on Both Sides:
Identity: an equation that has infinitely many solutions.
Infinitely Many Solutions: An equation that is true for any and every possible value.
No Solution: an equation has no solution if there is no value to make the equation TRUE.
GOAL:
We can find the solution to equations that have variables on both sides of the equal sign by using inverse operations and moving the smallest coefficient to the other side of the equal sign:
A dance studio charges $50 sign-up fee and $65 per day to take all dance classes. Another studio charges a $90 sign-up fee and only $45 per day to take all classes. For what number of days is the cost of the two dance studios the same?
SOLUTION: Using the given info we have:
Studio 1 $50 sign-up fee +50
Studio 2 $90 sign-up fee +90
Studio 2 $45 per day 45x
Studio 1 $65 per day 65x
Equal 65x + 50 = 45x + 90
65x + 50 = 45x + 90
65x + 16 = 45x + 90 Like terms on same side of equ. -45x -45x
20x + 16 = 90 -16 -16 Inverse of add
x = 4 days
20x = 74 Inverse of multiply 20x /20= 74/20
YOU TRY IT:
What is the solution of
5X – 1 = X + 15?
Solving equations with Distributive Property:
Ex: What is the solution of
4(2y+1)=2(y -13)?
To solve equations that include distributive property, we must distribute first, then isolate: