How many Solutions?
How many solutions does the equation have?
x + 2 = 2
Write and solve an equation to represent the scenario:
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A’s?
70m = 50m+500
It will take 25 months until Plan B with the phone costs the same as Plan A.
Which property justifies the step taken?
2x + 1 = 5x - 3
1 = 3x - 3
Subtraction POE
What is the term for the number in front of a variable
Coefficient
How many solutions does the following equation have?
3(2x - 5) = 6x - 5
No solutions.
Write and solve an equation to represent the scenario.
Find the value of x so that the triangle and rectangle have the same perimeter.
Triangle Side 1: (x+6) Side 2: (x+9) Side 3: (x+3)
Rectangle length: x+4 Rectangle width: x+1
x = 8
A student solved the equation 8x - 6 = -2(x + 8) as shown below. What justification did the student use to go from Line 1 to Line 2?
Equation
Line 1: 8x - 6 = -2(x + 8)
Line 2: 8x - 6 = -2x - 16
Line 3: 10x - 6 = -16
Line 4: 10x = -10
Line 5: x = -1
distributive property
Solve
-6x + 10 = 2(x + 17)
x = -3
How many solutions does the equation have?
12x + 5 = 2 + 3(9x+1)
ONE SOLUTION
x=0
Pearl bought a bag of treats for her cat. She writes an equation to represent the amount of treats remaining.
T = 45 - 3x
What could be the meaning of 45?
The amount of treats she started with.
The steps to correctly solve an equation are shown. Justify each step by determining which property was being utilized.
Equation Justification
Step 1: -3(x + 5) + (4x + 2) = 8 Original Equation
Step 2: -3x - 15 + 4x + 2 = 8
Step 3: x - 13 = 8
Step 4: x = 21
Step 2: distributive property of multiplication
Step 3: combining like terms
Step 4: subtraction property of equality
-5(3x + 4) = -7x + 28
x= -6
How many solutions does the equation have?
-5(3x + 4) = -7x + 28
ONE
x = -6
Sandra makes necklaces and sells them at a school craft fair. She uses the equation
P = 7.5n - (2.25n + 15) to determine her total profit, in dollars, at the fair when n necklaces are sold.
Based on this equation, how much does she charge for each necklace?
Sandra charges $7.50 for each necklace that she sells at the school craft fair.
Justify the steps for solving the inequality shown.
Inequality Justification
Step 1: 2x + 8 - 3x > ⅓(3x - 6) Original Equation
Step 2: 2x + 8 - 3x > x - 2
Step 3: -x + 8 > x - 2
Step 4: -2x + 8 > -2
Step 5: -2x > -10
Step 6: x < 5
Step 2: distributive property of multiplication
Step 3: combining like terms
Step 4: subtraction property of equality
Step 6: division property of equality, reversed the inequality symbol
Camila solved an equation but her final step is: 12 = 0.
Assuming she's made no mistakes, how many solutions does her equation have?
no solutions
How many solutions does the equation have?
3/4x+1=-3/4x+5
ONE!
Write and solve an equation to represent the scenario.
Marlo has $28 and is saving $13 per month. Kenya has $52 and is saving $7 per month. When will Marlo have the same amount of money saved as Kenya?
5 months
The steps to correctly solve an equation are shown. Justify each step by determining which property was being utilized.
Equation Justification
Step 1: 4(x + 7) = 9x - 7 Original Equation
Step 2: 4x + 28 = 9x - 7
Step 3: 28 = 5x - 7
Step 4: 35 = 5x
Step 5: 7 = x
Step 2: distributive property of multiplication
Step 3: subtraction property of equality
Step 4: addition property of equality
Step 5: division property of equality
Solve
1/2(4x - 2) - 8 = 3 - (x - 9)
x=7
What value of n would create an equation with infinitely many solutions?
7(2x - 3) = 14x + n
n = -21
A triangle and a rectangle have the same perimeter. Given the dimensions below, what must be the perimeter?
Triangle Side 1: (x+6) Side 2: (x+9) Side 3: (x+3)
Rectangle length: x+4 Rectangle width: x+1
Perimeter = 42
2(8+4)+2(8+1)=2(12)+2(9)=24+18=42
x=8
Solve the equation. Justify your steps using algebraic properties:
-5(x + 3) - 6 = x + 3
Step 1: -5x-15-6 = x+3 distributive property
Step 2: -5x-21 = x+3 combining like terms
Step 3: -6x-21 = 3 subtr POE
Step 4: -6x = 24 addition POE
Step 5: x = -4 division POE
Give the value of "b" that will result in infinite solutions.
2x + 6 = 2(x + b)
3