1. 1) Solve 2x - 4y = 7 for x + 4y + 4y 2x = 7 + 4y 2 2 Draw “the river”
D U
1) Solve 2x - 4y = 7 for x
· 2
-4y
+4y
÷ 2
+ 4y + 4y
2x = y
Draw “the river”
Add 4y to both sides
Simplify
Divide both sides by 2
Does it simplify?
This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

2. Let’s look at another example:
2Q-c = d
Multiply both sides by 2.
      
Subtract ‘c’ from each side.

3. 2) Solve 2x - 4y = 7 for y - 2x - 2x -4y = 7 - 2x -4 -4
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2) Solve 2x - 4y = 7 for y
· -4
+2x
-2x
÷ -4
- 2x x
-4y = 7 - 2x
Draw “the river”
Subtract 2x from both sides
Simplify
Divide both sides by -4
Does it simplify?
Nope!

4. Example 2B: Solving Formulas for a Variable
The formula for a person’s typing speed is
,where s is speed in words per minute,
w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.
Locate e in the equation.
Since w–10e is divided by m, multiply both sides by m to undo the division.
ms = w – 10e
Since w is added to –10e, subtract w from both sides to undo the addition.
–w –w
ms – w = –10e

5. 3) Solve for y: y + a = 3c -a -a y = 3c - a Draw “the river”
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3) Solve for y:
+ a
÷ 3
· 3
- a
Draw “the river”
Clear the fraction – multiply both sides by 3
Simplify
Subtract a from both sides
y + a = 3c
-a -a
y = 3c - a

6. Check It Out! Example 2
The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.
f = i – gt
Locate i in the equation.
f = i – gt
+ gt gt
Since gt is subtracted from i, add gt to both sides to undo the subtraction.
f + gt = i

7. 4) Solve for y: 4x – 2y = 12 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x
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4) Solve for y: 4x – 2y = 12
· -2
+ 4x
- 4x
÷ -2
- 4x x
-2y = 12 – 4x
y = x
or y = 2x - 6
Draw “the river”
Subtract 4x from both sides
Simplify
Divide both sides by -2
Does it simplify?
Yes!

8. Check It Out! Example 3a
Solve 5 – b = 2t for t.
5 – b = 2t
Locate t in the equation.
Since t is multiplied by 2, divide both sides by 2 to undo the multiplication.

9. Check It Out! Example 3b
Solve for V
Locate V in the equation.
Since m is divided by V, multiply both sides by V to undo the division.
VD = m
Since V is multiplied by D, divide both sides by D to undo the multiplication.

10. Lesson Quiz: Part 1
Solve for the indicated variable. 1. 2.
3. 2x + 7y = 14 for y 4.
for h
P = R – C for C
C = R – P
for m
m = x(k – 6 ) 5.
for C
C = Rt + S

11. Lesson Quiz: Part 2
Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.
6. Solve Euler’s formula for F.
F = 2 – V + E
7. How many faces does a polyhedron with 8 vertices and 12 edges have? 6