Equivalent Equations1
What does it mean for two (or more) equations to be equivalent?
Two (or more) equations are equivalent if they have the same solution(s).
Are these equations equivalent?
x + 2 = 7 and 2x + 1 = 11
YES
True or False:
x + 2 = 7 and x - 5 = 0 are equivalent equations.
True
What is an equation equivalent to x=5?
Answers may vary
2x=10 or 3x=15 or 4x=20
What does it mean for a number to be a solution to an equation?
A number is a solution to an equation when you plug that number into the equation it makes the equation true
What equation is equivalent to x+1=0
x=-1 or 2x+2=0 or 3x+3=0
Create an equation that is equivalent to: 2x + 4 = 19
Answers may vary
Are these equations equivalent?
2x + 4 = 20 and 2x + 7 = 23
Yes; x=8
Explain why an x value that makes Equation 1 true does not make Equation 2 true.
Equation 1: 2x + 4y = 12
Equation 2: x + 4y = 3
Because the two equations are not equivalent (therefore, they don't have the same solutions).
Are these equations equivalent?
1/2x+3/2=7/2
and
1/4x+3/4=7/4
Yes; x=4