Solving for x. Find the solution.
30 = 2(x + 3)
x = 12
−9(1 − y)
-9 +9y
Here is Caleb’s work writing the expression 5 − 3x + 11 − 9x with fewer terms.
Describe the mistake that Caleb made
Responses vary. • Caleb combined 16 − 6x to be 10x, but they can't be combined. • Caleb subtracted 3x − 9x instead of ‐3x − 9x.
5(x - 2) + 3x + 6
8x - 4
Write and equation that represents the following. Zahra buys 4 pens and a binder for $12. She pays a total of $19.
HINT: Draw a tape diagram and then write the equation.
12 + 4x = 19 (or equivalent)
‐4x − 17 = ‐5
x = ‐3
Write 24a − 18 in factored form.
2(12a − 9) or 6(4a - 3) (or equivalent)
Kwame and Maia each solved the same equation but used different strategies to do so.
Kwame began by distributing first.
Maia began by dividing each side by `3.3`.
18x - (7 + 4x)
14x - 7
Jamar delivers sandwiches for a restaurant. The restaurant charge $9.50 for each sandwich, plus an $8 delivery fee. Jamar has an order that totals $65.
HINT: Draw a tape diagram and then write the equation.
9.50x + 8 = 65 (or equivalent)
3(x - 7) = 33
x = 18. Work varies.
Write ‐ 1 —3 (9x − 15) in expanded form.
3x + 5 (or equivalent)
Vicente and Zwena are trying to write 9x-2x+4x using fewer terms.
Vicente rewrites it as 3x
Zwena rewrites it as 11x
Who is correct? Why?
Zwena
The subtraction symbol in front of the 2x applies only to the 2x and not to the terms that come after it.
4(-7a – 5) + 6(1 – 6a)
-64a - 14
Neena is saving money. She currently has $58 saved and earns $8 for every lawn she mows. Write an expression to represent how much money Neena has after mowing x lawns.
HINT: Draw a tape diagram and then write the equation.
8x + 58 (or equivalent)
3 + 5(x - 1) = 48
x = 10. Work varies
Factor the following expression
12a − 24
12 (a − 2)
Diego solved the equation -3(x + 6) = 21. His response is shown. Diego made a mistake. Identify his mistake, and then correct his response. Show or explain your thinking.
When solving the equation, Diego incorrectly distributed the -3 to the terms in parentheses. -3 ⋅ 6 is -18.
-(v – 5) – 3v(v + 1)
-4v + 5 – 3v2
A workout class charges each student $12 to attend, plus a towel rental fee. Today, 5 students paid $75 to attend the class.
HINT: Draw a tape diagram and then write the equation.
4 (x+5) = 75 (or equivalent)