6x 3 5x 7 6x 3 6x 7 6x 3 6x 3 One Solution No Solution and Infinitely Many Solutions 6x 3 5x 7 Things to notice about one solution equations Notice that there are a different quantity of xs on each side of the equation ID: 317303
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Slide1
Equations with One Solution, No Solution, and Infinitely Many Solutions
6x + 3 = 5x + 7
6x + 3 = 6x + 7
6x + 3 = 6x + 3Slide2
One Solution, No Solution, and Infinitely Many Solutions
6x
+ 3 = 5x +
7Things to notice about one solution equations:Notice that there are a different quantity of x’s on each side of the equation.Let’s Solve…Slide3
One Solution, No Solution, and Infinitely Many Solutions
6x
+ 3 = 5x +
7
4 is the ONLY value of x that makes the equation true, therefore there is only ONE
SOLUTION.
-5x -5x
X + 3 = 7
-3 -3
X = 4Slide4
One Solution, No Solution, and Infinitely Many Solutions
One Solution
X = 5
a different quantity of x’s on each side of the equation.
Problem Type Result Type Keys to Look ForSlide5
One Solution, No Solution
, and Infinitely Many Solutions
6x + 3 = 6x + 7
Things to notice about no solution equations:Notice that there are the SAME quantity of x’s on each side of the equation but a different constant on each side.
Let’s Solve…Slide6
One Solution, No Solution
, and Infinitely Many Solutions
6x + 3 = 6x + 7
Since 3 does NOT equal 7 we know that there is NO SOLUTION that will make this equation true!-6x -6x
3 = 7 ???Slide7
One Solution, No Solution, and Infinitely Many Solutions
One Solution
X = 5
a different quantity of x’s on each side of the equation.
No Solution
3 = 7
the
SAME
quantity of x’s on each side of the equation but a different constant on each side
Problem
Type Result Type Keys to Look ForSlide8
One Solution, No Solution
,
and
Infinitely Many Solutions6x + 3 = 6x + 3Things to notice about infinitely many solution equations:Notice that there are the same quantity of
x’s on each side of the equation AND the same value of constants.
Let’s Solve…Slide9
One Solution, No Solution
,
and
Infinitely Many Solutions6x + 3 = 6x + 3-6x -6x
3 = 3 ???
Since
the quantity of x’s cancel each other out, we
know that
any value of x will
make this equation true! If the constants have the same value, the equation is said to have INFINITELY MANY SOLUTIONS!Slide10
One Solution, No Solution, and Infinitely Many Solutions
One Solution
X = 5
a different quantity of x’s on each side of the equation.
No Solution
3 = 7
the
SAME
quantity of x’s on each side of the equation but a different constant on each side
Infinitely Many Solutions3 = 3
the same quantity of x’s on each side of the equation AND the same value of constants. Problem
Type Result Type
Keys
to Look ForSlide11
One Solution, No Solution, and Infinitely Many Solutions
Challenge Question!
Solve The Following Equation Completely, Tell Whether It Has One Solution, No Solution, Or Infinitely Many Solutions and Explain Why:
3(2x + 4) = 6(x + 2)Slide12
One Solution, No Solution, and Infinitely Many Solutions
Challenge Question!
3(2x + 4) = 6(x + 2)
Use the Distributive Property6x + 12 = 6x +12Notice the same quantity of x’s on each side of the equation AND the same value of constants but solve completely anyway…12 = 12
Infinitely Many Solutions!Slide13
One Solution, No Solution, and Infinitely Many Solutions
Group Activity:
Write one equation that has
one solution, one equation that has no solution, and one equation that has infinitely many solutions. Trade with a neighbor and check their work. Without solving, discuss whether each problem is correct or incorrect and be prepared to explain why.