1. Warm-Up Solve each equation. Show your work and check the solution.
–6x = – 42
6 = 8 + y
p = –12
h = 24.7
x = 7
y = –2

2. A.1.8
Solving Equations

3. Example 1
Deborah opened an ice cream stand at the local pool last summer. She spent $148 on a freezer to start her business. She earned a profit of $0.75 for each ice cream cone she sold. She earned a total of $452 during the summer. How many ice cream cones did Deborah sell? Write the equation: Add 148 to both sides. Divide each side by  Check the solution. Deborah sold 800 ice cream cones last summer.
0.75x – 148 = 452
0.75x = 600
x = 800
0.75(800) –
600 –
452 = 452

4. Example 2
Solve the equation for the variable. Check the solution. Write the equation. Subtract 2 from both sides of the equation. Multiply each side by 7.  Check the solution. x = –56 –2 –2

5. Example 3
Solve the equation for x. Check the solution. 12 – 5x = 2 Rewrite the equation by adding the opposite. Subtract 12 from both sides. Divide each side by (–5).  Check the solution x = 2
12 + (–5x) = 2
– –12
–5x = –10
x = 2
12 – 5(2) = 2
12 – 10 = 2
2 = 2 –5 –5

6. A.1.8 Practice
Solve each equation. Show your work and check the solution. 1. 2x – 8 = –5 = m + 4 = 7 4. –8 + = 2
x = 10
y = –18
m = 5
b = 60

7. A.1.8 Formative 3
Solve each equation. Show your work and check the solution. 1. 4x – 5 = –2 = m + 16 = –1 + = 24
x = 10
y = –16
m = 5
b = 100

8. Warm-Up Solve each equation. Check your solution. –9x – 21 = 24 x = –5
–3m + (–7m) + 2m = –80
(Hint: Combine like terms and then solve)
x = –5
y = 0.5
m = 10

9. Solving Equations with a single variable occurring more than once
Simplify and solve equations for a single variable occurring more than once in the equation using inverse operations.

10. Solving Equations with a single variable occurring more than once
Start by clearing one of the variables (if you can) using inverse operations to make a two-step equation.
2x - 11 = -8x + 89
Clear the constant.
10x – 11 = 89
Solve the one-step equation.
10x = 100

11. Example 1
Solve the equation for the variable. Check the solution. a. 3x – 26 = 7x + 2 a

12. Example 2
Solve the equation for the variable. Check the solution. b. 6m + 22 = – 2m + 10 a

13. Example 3 a

14. Example 4 a

15. Example 3
The Underwood family is 340 miles away from home and are headed toward home at a rate of 52 miles per hour. The Underwoods’ next-door neighbors, the Jacksons, are leaving home, traveling towards the Underwoods’ at a rate of 48 miles per hour. How long will it be before they pass each other?
Let h represent the number of hours the two families have been on the road.
The expression that represents the Underwoods’ distance from home is 340 – 52h. The expression that represents the Jacksons’ distance from home is 48h.
Set the two expressions equal to one another.
Add 52h to both sides.
Divide each side by 100.
The Jackson and Underwood families will pass each other after 3.4 hours.
340 – 52h = 48h
+52h h
340 = 100h
3.4 = h a

16. Communication Prompt
What do you think is most important to remember when solving equations?

17. A.1.8 Formative 4 Part 1
Solve each equation. Show your work and check the solution. 1. –10x + 5 = = m – 6 = = –8
x = –3
y = –8
m = 50
b = –200

18. A.1.8 Formative 4 Part 2
x = 5
p = – 4
x = -10.5
n = 2

19. Warm-Up Solve each equation for x. 1. 33 = 5(x + 8) + 3 x = 2
2. 2m + 3(m – 8) = 1
3. 3x + 10 = 9x – 26
x = 2
m = 5
x = 6

20. Solving Linear Equations
Determine if a linear equation with one variable has no solution, one solution or infinitely many solutions.

21. Underwood Family y = 340-52h Jackson Family y = 48h

22. Determining the Number of Solutions to a Linear Equation
A linear equation with one variable has…
One solution : when solved, the variable is equal to one number. ( x = 8.5 )
No solution when solved, the variables are eliminated and the end result is a false statement (10 = -15)
Infinitely many solutions when solved, the variables are eliminated and the end result is a true statement that will ALWAYS be true. (14=14)

23. Example 1
Solve for x. Describe the number of solutions.

24. Example 2
Solve for x. Describe the number of solutions.

25. Example 3
Solve for x. Describe the number of solutions.

26. Communication Prompt
What does it mean when an equation has infinitely many solutions?

27. A.1.8 Formative 5
Solve each equation. State whether there is one solution, no solutions, or infinitely many solutions.
2x + 6 = 6x  22
2x + 8 = 2x  3
3(x – 4) = x + 2x – 12
x = 7;
one solution
8 = 3;
no solutions
−12 = −12;
infinitely many solutions