Download 1 - RCSD

3-1 Interpreting Algebraic Expressions
Name______________________________________
Level 4: I can solve linear equations in one variable with coefficients represented by letters.
Level 3: I can solve linear equations in one variable.
Level 2: I can solve an equation that requires more than one step and explain why each step is valid.
Level 1: I can determine whether a given value of x makes an equation true or false.
1.
Describe the property used to convert the equation from one line to the next:
(
)
x 1- x +2x - 4 = 8x -24- x 2
Given equation
x - x2 +2x - 4 = 8x -24- x2
x +2x - 4 = 8x -24
3x - 4 = 8x -24
3x +20 = 8x
20 = 5x
What is the common solution set to all these equations?
For each of the following statements, indicate whether it is ‘Always true’, ‘Never true’ or ‘Sometimes true’. Circle the
correct answer. If you choose ‘Sometimes true’ then state on the line below when it is true. The first one is done for you
as an example.
2. x +2 = 3
Always true
Never true
Sometimes true
When x =1
3. x -12 = x +30
Always true
Never true
Sometimes true
(
)
Always true
Never true
Sometimes true
3 x -2 = 3x -2
(
)
Always true
Never true
Sometimes true
6.
( x + 4) = x
Always true
Never true
Sometimes true
7.
x2 + 4 = 0
Always true
Never true
Sometimes true
4.
2 x +6 = 2x +12
5.
2
2
+ 42
Name a value of the variable that would make each equation a true number sentence.
8.
7+ x =12 is true when _______________.
9. 3x + 0.5 =
37
is true when _______________.
2
10. x 3 = -125 is true for _______________.
11. A number x and its square, x 2 have the same value
when _______________.
12. x 2 = -9 is true when _______________.
13. Let _______________, then 2a = a+a is true.
14. x +67 = x +68 is true for _______________.
15. x 2 = 9 is true when _______________.
16. Consider the equation 3x + 4 = 8x -16 . Solve for x using the given starting point.
Group 1
Subtract 3x from both
sides
3x + 4 = 8x -16
Group 2
Subtract 4 from both
sides
3x + 4 = 8x -16
Group 3
Subtract 8x from both
sides
Group 4
Add 16 to both sides
3x + 4 = 8x -16
3x + 4 = 8x -16
17. Consider the equation, x 2 = 3x + 4 , where 𝑥 represents a real number.
Are the expressions x 2 and 3x + 4 algebraically equivalent?
What value of x makes the equation true?
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)
18. Solve for x : x 3+ x = 3x + x 2 .
Create an expression for the right side of each equation such that the solution set for the equation will be all real numbers.
19. 2x -5=
(
20. x 2 + x =
)
2
21. x + 2 =
Generate the following:
22. An equation that is always true
23. An equation that is true when x = 0
24. An equation that is never true
25. An equation that is true when x =1 or x = -1
26. Verify that x =1, x = -1 , and x = 2 are each solutions to the equation x 3 +2 = 2x2 + x .
(
)
27. 2 6x + 8 = 4+6x
(
)(
)
30. x -1 x + 5 = x 2 + 4x -2
(
)
28. x 2 - 4x + 4 = 0
29. 39- 8x = -8 3+ 4x + 3x
31. -7-6x +5x = 3x -5x
32. 7-2x =1-5x +2x