1-5 Exploration Activity
Equations
Name:____________________________
1. Referring back to section 1.1, what is an algebraic expression?
2. What mathematical symbol is represented in any equation that is not in an expression? (Refer to Pg. 33)
a. ___________________________
3. Using your characteristics from above, develop a definition from an equation using your own words.
Your Definition of Equation:
a. Referring to section 1.5 in your book (Pg.33), how does your book define an equation?
b. How is your definition for equation similar to the textbook definition? How is it different?
4. Algebraic expression vs. Equation. In section 1.5 (Pg.33), how is an algebraic expression and an equation
related?
Evaluate the following. Then explain what operation you used and why?
5. 4+16
6. 11-3
Explain:
7. 5∙6
Explain:
8.
24
2
Explain:
Explain:
Solve for the missing variable. Then explain what operation you used and why?
9.
Explain:
x+16=20
10. y-3=8
11. Z∙6=30
Explain:
Explain:
12.
𝑥
2
= 12
Explain:
13. What do we notice about the operations that we are performing in #5-8 and the operations that we are performing
in #9-#12?
Now were going to get more challenging!
14. Write a verbal expression for 5𝑥 + 3 = 18. ___________________________________________________________
a. Using logic, what number x will make our verbal expression true? x= __________
15.
List our order of operations in the their order.
P= ____________ E= ____________ M=___________
D= __________
A= __________
S= __________
16. Solve for x: 5(3) + 3 = 𝑥.
a. What operation did you perform first? __________________________
b. What operation did you perform second? _______________________
17. The following number x is solved for us. List the operations that were used to solve this equation.
5x + 3 = 18
-3
-3
5x=15
1. ___________________________
2. ___________________________
5 5
x=3
18. What do we now about the order of operations that we used in #16 compared to #17?
Exercises
𝟏 𝟏
𝟒 𝟐
Determine which x and y values make each equation true if x = { , , 𝟏, 𝟐, 𝟑} and y = {2, 4, 6, 8}.
1
5
19. x + 2 = 2
20. x + 8 = 11
21. (𝑦 + 1)2 = 9
Solve each equation for the specified variable.
22. (18 + 4) + 𝑚 = (5 − 3)𝑚
23. 𝟖 ∙ 𝟒 ∙ 𝒌 + 𝟗 ∙ 𝟓 = (𝟑𝟔 − 𝟒)𝒌 − (𝟐 ∙ 𝟓)