Comparing Expression (Answer As A Question!)
A symbolic representation of a number that is unknown, usually represented by a letter.
What is a variable?
A mathematical statement that shows a comparison of two values in which one number is either less than (<), greater than (>), less than or equal to (<=), or greater than or equal to (>=) the other number.
What is an inequality?
Solve the following equation:
5x - 1 = 4
x = 1
Determine if the following equation has one, infinitely many solutions, or no solutions:
x = x
The equation has infinitely many solutions.
Solve the following equation:
4x - 1 = 15
x = 4
A mathematical statement that includes constants (numbers) and unknown values (like "x") as terms (being added or subtracted together).
What is an expression?
This inequality has a graph with an open circle and an arrow pointing to the left from positive 3.
What is x < 3?
Solve the following equation:
12x + 36 = -12x - 36
x = -3
Determine if the following equation has one, infinitely many or no solutions:
3x-1 = 2x+4
The equation has one solution.
Solve the following equation:
2x + 1 = 3x -2
x = 3
This is created when two algebra tiles identical to each other, but opposite in sign, are combined together on the same side of the mat to yield 0.
What is a "zero pair"?
This inequality has a graph with a closed circle and an arrow pointing to the right from negative -10.
What is x>= -10?
Solve the following equation:
6x + 12 = 3x+ 36
x = 8
Niko was given following equation: 2x - 3 - x + 1 = 2x + 3 - x + 1
He was asked to determine the number of solutions, and he gave the following answer: There are infinitely many solutions.
Is Niko's answer correct? Explain your reasoning.
Niko's answer is incorrect because:
1) 2x-3-x+1 = 2x+3-x+1
x - 2 = x + 4 (Combine like terms.)
-2 ≠ 4 (Subtract "x").
This equation has no solution, not infinitely many solutions.
2) Without using inverse operations, you may also note that both equations are not the same (there is a "+3" on the left and a "-3" on the right.)
Solve the following equation:
5x - 8 = 5x - 8
0 = 0 (Infinitely many solutions.)
This is created when two algebra tiles identical to each other are removed from opposite sides of the mat.
What is a "matching set"?
This number indicates the starting point for the set of values that make the statement true.
What is a boundary point?
Solve the following equation:
3x - 5 = 3x + 6
0 ≠ 1 (No solution.)
Determine if the following equation has one solution, infinitely many solutions, or no solution:
3x + 3 - 9x + 6 = 18x + 3 - 24 x + 5
This equation has no solution.
Solve the following equation:
10x + 120 = 10x + 121
0 ≠ 1 (No solution.)
Since x represents an unknown value, meaning it can take on any value (positive, negative, or 0), we are not able to do this particular task.
Why can "x" not be compared to a number using >, <, or =?
This is used when the boundary point is included as a part of the set of solutions that make the inequality true.
What is a closed circle?
Solve the following equation:
100x + 250 = 100x + 250
0 = 0 (Infinitely many solutions.)
Determine if the following equation has one solution, infinitely many solutions, or no solution:
5x - 7 - 2x + 1 = 2x + 4 + x - 10
This equation has infinitely many solutions.
Determine if the following equation has one solution, infinitely many solutions, or no solution:
(3/5)x - 5 = (3/5)x - 4
This equation has no solution.