Combining Like Terms
Simplify 3x + 4x
7x
Expand: 2(x + 5)
2x + 10
Solve: 3x + 5 = 20
x = 5
If three times a number increased by 5 is 20, what is the number?
Equation: 3x + 5 = 20
Answer x = 5
Describe the solution type of x = 5x
One Solution
Simplify: 5x + 3 − 2x + 7
3x + 10
Expand: 3(x − 2)
3x - 6
Solve: 4x - 6 = 10
x = 4
Sam has twice as many pencils as Rachel. If Rachel has 5 fewer pencils than Sam, how many pencils does Sam have?
Equation: 2x = x + 52x
Answer: Sam has 10 pencils
Explain why a = a has infintely many solutions.
Becuase it is always true, regardless of the value of a.
Combine like terms: 8x − 3y + 4x + 5y
12x + 2y
Expand and simplify: 4(x + 3) + 2x
6x + 12
Solve: 3(x + 2) = 12
x = 2
A rectangle's length is 3 times its width, and the perimeter is 48 cm. Find the width.
Equation: 2(3x + x) = 48
Answer: Width = 6 cm
Why does 5 = 8 mean there is no solution.
It's a false statement with no values of x that make it true.
Simplify: 2(x+4) + 3x − 2
5x + 6
Use the Distributive Property: 2(3x - 1) - 4x
2x - 2
Sovle: 5x - 2(3x + 1) = 9
x = 7
A group of friends spends $50 on snacks, and each person contributes $5. How many people are in the group?
Equation: 5x = 50
Answer: There are 10 people in the group.
Given 3x + 5 = 3x + 8, how many solutions does it have?
No solutions, because it simplifies to 5 = 8
Simplify: 6x − 4 + 2(3x+1)
12x - 2
Expand and combine terms: 5(x - 4) + 3(2x + 1)
11x - 17
Solve: 2(x + 4) - 3(x - 1) = 7
x = 5
A cell phone plan costs $30 plus $0.10 per text. If the total bill is $50, how many texts were sent?
Equation: 30 + 0.10x = 50
Answer: 200 texts
Write an equation that has one solution, no solutions, and infintely many solutions.
Examples:
One Solution: x + 3 = 5
No Solutions: x + 2 = x + 3
Infintely Many Solutions: 2x + 4 = 2(x + 2)