TERMS & VOCABULARY
Clue: A letter or symbol used to represent an unknown value.
Answer: Variable
x+7=15
x=8
A student solves:
x + 6 = 11 by doing: x = 11 + 6
What did the student do incorrectly?
Answer: They should use the inverse operation.
Subtract 6:
x=11−6
y=3x+5
What is m and what is b?
m=3 (slope)
b=5 (y-intercept)
Find the common difference: 4, 9, 14, 19,…
d=5
Consider:
7x−4
What is the coefficient?
Answer:
7
3x−5=16
x=7
Can these terms be combined?
4x+3y
Explain why or why not.
Answer: No.
They are not like terms because x and y are different variables.
Is this line increasing or decreasing?
y=−4x+2
Decreasing: A negative slope means the line decreases from left to right.
Find the next two terms: 30, 24, 18, 12,…
6, 0
Classify:
4x+9
Is it an expression, equation, or inequality?
Answer: Expression
Why: It has no equal sign or inequality symbol.
2(x+4)=18
x=5
Why do we subtract 7 from both sides here?
3x+7=22
Answer: To keep the equation balanced/equal while isolating the variable.
3x+7−7 = 22−7
y= -2/3x + 4y
identify the slope and explain the rise/run.
Find the missing value: 12, 19, ___, 33, 40
26
Consider:
5x+3y−8
Identify: a variable, a coefficient, the constant, and the number of terms
Answer:
5x+2=3x+14
x=6
A student says:
4x+8=20 so x=16
Explain the error and solve correctly.
The student did not correctly use inverse operations.
x=3
Rewrite in slope-intercept form:
2x + y = 7
Then identify m and b.
m=−2
b=7
Write the explicit rule for: 5, 8, 11, 14,…
Use: Value = d(n)+ b
Value= 3n + 2
Example: 3(1) + 2 = 5
Explain the difference between an: Expression and Equation
An expression contains numbers, variables, and operations but does not make a comparison.
An equation states that two expressions are equal.
7x−9=3x+19
x=7
A student solves:
6x+4 = 2x+20 like this: 8x=24
x=3
What was the error?
You cannot simply combine 6x and 2x across an equal sign. You have to subtract either one, not add.
Find the slope between: (2,3) and (6,11)
Use: (y2 - y1 / x2 - x1)
m=2
A student has $20 and saves $6 each week.
Write a rule for the amount of money after w weeks.
M = 6w + 20