1. 10-5 Solving for a Variable Warm Up Problem of the Day
Lesson Presentation
Pre-Algebra

2. PA HOMEWORK Answers
Page 517 #14-26 EVENS

3. Pre-Algebra HOMEWORK
Page 521
#1-11 ALL
NO WORK= ZERO CREDIT!

4. Our Learning Goal
Students will be able to solve multi-step equations with multiple variables, solve inequalities and graph the solutions on a number line.

5. Our Learning Goal Assignments
Learn to solve two-step equations.
Learn to solve multistep equations.
Learn to solve equations with variables on both sides of the equal sign.
Learn to solve two-step inequalities and graph the solutions of an inequality on a number line.
Learn to solve an equation for a variable.
Learn to solve systems of equations.

6. Today’s Learning Goal Assignment
Learn to solve an equation for a variable.

7. Remember!!!
If an equation contains more than one variable, you can sometimes isolate one of the variables by using inverse operations.
You can add and subtract any variable quantity on both sides of an equation.

8. Additional Example 1A: Solving for a Variable by Addition or Subtraction
Solve for the indicated variable.
A. Solve a – b + 1 = c for a.
a – b + 1 = c
Add b and subtract 1 from both sides.
+ b – b – 1
a = c + b – 1
Isolate a.

9. Try This: Example 1A
Solve for the indicated variable.
A. Solve y – b + 3 = c for y.
y – b + 3 = c
Add b and subtract 3 from both sides.
+ b – b – 3
y = c + b – 3
Isolate y.

10. Additional Example 1B: Solving for a Variable by Addition or Subtraction
Solve for the indicated variable.
B. Solve a – b + 1 = c for b.
a – b + 1 = c
Subtract a and 1 from both sides.
– a – – a – 1
–b = c – a – 1
Isolate b.
–1  (–b) = –1  (c – a – 1)
Multiply both sides by –1.
b = –c + a + 1
Isolate b.

11. Try This: Example 1B
Solve for the indicated variable.
B. Solve p – w + 4 = f for w.
p – w + 4 = f
Subtract p and 4 from both sides.
– p – – p – 4
–w = f – p – 4
Isolate w.
–1  (–w) = –1  (f – p – 4)
Multiply both sides by –1.
w = –f + p + 4
Isolate w.

12. As the equations get more complicated…. REMEMBER…
To isolate a variable, you can multiply or divide both sides of an equation by a variable if it can never be equal to 0.
You can also take the square root of both sides of an equation that cannot have negative values.

13. Additional Example 2A: Solving for a Variable by Division or Square Roots
Solve for the indicated variable. Assume all values are positive.
A. Solve A = s2 for s.
A = s2
√A = √s2 Take the square root of both sides.
√A = s Isolate s.

14. Try This: Example 2A
Solve for the indicated variable. Assume all values are positive.
A. Solve w = g2 + 4 for g.
w = g2 + 4
– – 4 Subtract 4 from both sides.
w – 4 = g2
Take the square root of both sides.
√w – 4 = √g2
√ w – 4 = g Isolate g.

15. Additional Example 2B: Solving for a Variable by Division or Square Roots
Solve for the indicated variable. Assume all values are positive.
B. Solve V = IR for R.
V = IR
= Divide both sides by I. IR I V I V
= R Isolate R.

16. Try This: Example 2B
Solve for the indicated variable. Assume all values are positive.
B. Solve A = lw for w.
A = lw
= Divide both sides by l. lw l A l A
= w Isolate w.

17. Additional Example 2C: Solving for a Variable by Division or Square Roots
C. Solve the formula for the area of a trapezoid for h. Assume all values are positive.
A = h(b1 + b2) 1 2
Write the formula.
2  A = 2  h(b1 + b2) 1 2
Multiply both sides by 2.
2A = h(b1 + b2) 2A
(b1 + b2)
h(b1 + b2) =
Divide both sides by (b1 + b2). 2A
(b1 + b2)
= h
Isolate h.

18. Try This: Example 2C
Solve for the indicated variable. Assume all values are positive.
C. Solve s = 180(n – 2) for n.
s = 180(n – 2)
s (n – 2)
180 =
Divide both sides by 180. s
180
= (n – 2)
+ 2
+ 2
Add 2 to both sides. s
180
+ 2 = n

19. To find solutions (x, y), choose values for x substitute to find y.
Remember!

20. Additional Example 3: Solving for y and Graphing
Solve for y and graph 3x + 2y = 8.
3x + 2y =
–3x –3x x y
2y = –3x + 8 –2 7 4
–3x + 8 2 2y = 2 1
y =
–3x 2 4 –2

21. Additional Example 3 Continued
3x + 2y = 8

22. Try This: Example 3
Solve for y and graph 4x + 3y = 12.
4x + 3y = x y
–4x – 4x –3 8
3y = –4x + 12 4
–4x + 12 3 3y = 3 6 –4
y =
–4x 3

23. Try This: Example 3 Continued10 8 6
4x + 3y = 12 4 2 x
–4 – –2 –4 –6

24. Don’t forget your proper heading! Trade & Grade!
10-5 Lesson Quiz: Part 1
Solve for the indicated variable.
1. P = R – C for C.
2. P = 2l+ 2w for l.
3. V = Ah for h.
4. R = for S.
C = R - P
= l
P – 2w 2
= h 3V A 1 3
C – S t
C – Rt = S

25. 5. Solve for y and graph 2x + 7y = 14.
Lesson Quiz: Part 2
5. Solve for y and graph 2x + 7y = 14.
y = – 2x 7 y 4 2 –2 –4