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WorksheetsSolving Linear Equations and Concepts
Total questions: 92
Worksheet time: 46hrs 0mins
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📘 Beginning Algebra Quizlet Set: Are you ready??
No...
HELP
YES!
Well.........
Q: What is the goal in a linear equation?
To get x alone.
To get y alone
Q: Solve: x+6=15
x = 2
x = 0
x = -9
x = 9
Q: Solve: 3x+5=11
x = 6
x = 0
x = 6/1
x = 2
It's always a good idea to move (a) first.
(ex: 5x = 10)
What is our last step? (in equations)
Divide
Subtract
Multiply
Add
Rectangular Coordinates (the grid) What is it for?
To plot decimals
Plotting points and lines on the graph.
To make an equation seem correct
To simplify
Plot (2,3)
Left 3, up 2
Right 3, left 2
Up 2, left 3
Right 2, Up 3
Where is (0,4)?
On the x-axis, 4 units up
On the y-axis, 4 units up
X is... ___________
horizontal
vertical
Y is... ___________
horizontal
vertical
Which is correct?
( y , x )
( x, y )
Which of the following is true about the graph shown?
It has a positive rate of change.
It has an x-intercept at (9, 0).
It is non-linear.
It passes through the point at (1, 5).
Q: Steps to graph y=mx+b
A:
Start at b (y-intercept).
Use slope m (rise/run).
Plot 2+ points.
what's next?
Connect line
Divide the two points
X * everything on one side of the slope
Divide rise/run
Using slope is important because it helps find more ________
Decimals
Points
Do you understand this so far?
Yes
No
Here is the end of the question, do you have any problems?
Yes!
No!
Q: Formula for slope from 2 points? m= ___-___ / ___-___
(a)
Line is y=−3x+4 | What is m and b? |
m= −3, b = 4
m = 3, b = -4
Q: What does slope m = 2 mean?
Go right 2, up 1
Go up 2, right 1
Q: What does slope m = −1 mean?
Go down 1, right 1
Go up 1, right 1
Q: What does b = 5 mean in y = mx + 5
The line crosses y-axis at (0,5).
The line crosses x-axis at (5,0).
m = slope (rise/run)
y=mx+b
b = y-intercept (start point)
y=mx+b
Q: What do you do if you divide by a negative in inequalities?
Never flip the sign ( stays the same )
Flip the sign (< becomes >, etc).
LCD means...
(a)
How do you clear decimals?
Divide by 10 always
Add x to both sides
Keep it as a decimal, never clear it
Multiply by 10, 100, etc.
What does 25% mean?
50%, 0.5, or 50/1
25 out of 100, or 0.25.
Q: How to solve proportions?
Divide both sides by 1
Keep the lowest number of the graph
Add to both sides from x =
You need to Cross-multiply
Q: Solve: x−7=10
(a)
Solve: 3x+2=11
(a)
Solve: 2x−5=9
(a)
Q: Solve: −4x+3=7
(a)
Q: Solve: 2(x+4)=14
(a)
Q: Solve: 3(x+2)−5=2(x−1)+4
(a)
Q: Solve: − 2 ( x − 4 ) + 3 = x + 7
(a)
Do you understand this problem? ( please work it out to get the answer)
Yes
No
Q: Find slope between (1,2) and (3,6).
Remember that ( m = y2 - y1 / x2 - x1 )
(x1, y1) ( x2, y2)
(a)
Read them, work them out, ask questions! (questions are good!) then once you think you are ready or have a question, answer below.
I understand!
I don't understand, H.E.L.P....
What does "Rise over Run" mean?
Rise = how far you go ____ or ____
Up or Down
Left or Right
Rise = how far you go up or down. (Up =__________, Down = __________)
Up: Positive, Down: Negative
Up: Negative, Down: Positive
Run = how far you go ______ or ______.
Right or left
Up or down
Run = how far you go right or left. (Right = __________ , Left = ___________)
(a)
Slope m = rise/run (is this statement true or false?)
Think of slope as ....
Stairs
Brackets
The rise is how many steps you go (a)
The run is how many steps you go ...
(a)
Do you understand this problem? Work it out yourself, then answer!
I understand
I need help....
Review yourself, answer and then below choose how well you understand between 1-10
1-3
4-6
7-8
9-10
Do you understand this?
Yes
H . E . L . P
Rise = up/down ( _- change )
(a)
Run = left/right ( _ - change )
(a)
Slope is rise __ run
-
+
x
÷
Q: What’s slope if line is horizontal?
A (a) slope
Q: What’s slope if line is vertical?
A (a) slope
Equation of a line with slope 3 and y-intercept 2?
Remember ( y = mx + b )
y = 3x + 2
y = 2x + 3
Going up → slope positive.
Going down → slope negative.
Flat → slope zero.
Straight up/down → slope undefined.
TRUE OR FALSE
👉 If you can explain a topic out loud like you’re teaching a class, then you truly understand it.
Try this out on your own, step by step.
Yes if you did well, No if you need to review
Yes
No
Do you understand this?
Yes.
No.
Q: What does (a, b) mean?
A: All numbers between a and b, but not including a or b. (Edges are (a) 🚪)
Q: What does [a, b] mean?
A: All numbers between a and b, including a and b. (Edges are (a) 🚪)
parentheses mean “ (a) ,” no equals.
Q: Which inequality matches [a, b]?
A: a ≤ x ≤ b → brackets mean “ (a) the edges.”
Q: On a number line, how do you show (3, 7)?
A : (a) circles at 3 and 7, shade between them.
Q: On a number line, how do you show [3, 7]?
A: (a) circles at 3 and 7, shade between them.
Q: When do you use parentheses ( ) at infinity?
________ — because infinity goes on forever, you can’t “include” it. Example: (−∞, 5] or [2, ∞).
Never
Always
Q: What’s the difference between x < 5 and x ≤ 5?
x < 5 → (−∞, 5) → open circle at 5.
x ≤ 5 → (−∞, 5] → closed circle at 5.
x < 5 → (−∞, 5) → closed circle at 5.
x ≤ 5 → (−∞, 5] → open circle at 5.
Q: What symbol do we ALWAYS use with infinity?
___________ — because you can’t “reach” or “include” infinity.
( )
+
Do you understand this?
Yes
No
Q: How do you write “all numbers greater than 3”?
A: (3,∞) → open at 3, goes right forever.
A: [3,∞) → closed at 3, goes right forever.
Q: How do you write “all numbers greater than or equal to 3”?
A: [3,∞) → closed at 3, goes right forever.
A: (3,∞) → open at 3, goes right forever.
Q: What’s the difference between (−∞,5) and (−∞,5]?
A: The first excludes 5 (____ circle). The second includes 5 (____circle).
(a)
Q: What does (−∞,∞) mean?
A: All real numbers (the whole number line).
This is a false statement.
This is a true statement
Do you understand this?
Yes!
No!
Q: On a number line, what does a bracket [ ] mean?
A: A closed circle — you shade that number because it’s included (≤ or ≥).
Q: On a number line, what does a parenthesis ( ) mean?
A: An open circle — you do NOT shade that number because it’s excluded (< or >).
Q: How do you graph x < 3?
A: Put an _____ circle at 3 (since it’s <, not equal). Shade to the _____ (all numbers smaller than 3).
(a)
Q: How do you graph x ≤ 3?
A: Put a _____ circle at 3 (≤ means include). Shade to the ____.
(a)
Q: How do you graph x > -2?
A: Put an _____ circle at -2. Shade to the ____ (numbers greater than -2).
(a)
Q: How do you graph x ≥ -2?
A: Put a _____ circle at -2. Shade to the ______.
(a)
Graph (-∞, 3).
A: Open circle at 3, shade everything to the (a) .
Q: Graph [2, ∞).
A: Closed circle at 2, shade everything to the (a) .
Q: Graph [-2, 5).
A: Closed circle at -2, open circle at 5, shade the line (a) them.
Do you understand this?
Yes!!
H. E. L. P
Q: Write the interval for “x is greater than or equal to 2.”
[2, ∞)
(2, ∞)
Q: Write the interval for “x is less than 5.”
(-∞, 5)
(-∞, 5]
Q: Graph x ≤ 3 on a number line.
A: Shade left of 3, put a (a) circle on 3
Q: Graph x > -2 on a number line.
A: Shade right of -2, put an (a) circle on -2
Q: What does |x| mean?
A: The distance of x from 0 (always positive or zero).
Q: What is |-18|?
A: 18 (absolute value makes negatives positive).
Q: Solve |x| = 7.
A: Two answers: x = 7 or x = -7
Try and solve it on your own! If you need help, just ask questions
I need help...
I am all good!
