Transcript 11-3 - Tapp Middle School

Solving Equations with
11-3 Variables on Both Sides
Warm Up
Problem of the Day
Lesson Presentation
Course 3
Solving Equations with
11-3 Variables on Both Sides
Learn to solve equations with variables on
both sides of the equal sign.
Course 3
Solving Equations with
11-3 Variables on Both Sides
Some problems produce equations that have
variables on both sides of the equal sign.
Solving an equation with variables on both
sides is similar to solving an equation with a
variable on only one side. You can add or
subtract a term containing a variable on both
sides of an equation.
Course 3
Solving Equations with
11-3 Variables on Both Sides
Additional Example 1A: Solving Equations with
Variables on Both Sides
Solve.
4x + 6 = x
4x + 6 = x
– 4x
– 4x
6 = –3x
6 = –3x
–3
–3
–2 = x
Course 3
Subtract 4x from both sides.
Divide both sides by –3.
Solving Equations with
11-3 Variables on Both Sides
Additional Example 1B: Solving Equations with
Variables on Both Sides
Solve.
9b – 6 = 5b + 18
9b – 6 = 5b + 18
– 5b
– 5b
Subtract 5b from both sides.
4b – 6 = 18
+6 +6
4b = 24
4b = 24
4
4
b=6
Course 3
Add 6 to both sides.
Divide both sides by 4.
Solving Equations with
11-3 Variables on Both Sides
Additional Example 1C: Solving Equations with
Variables on Both Sides
Solve.
9w + 3 = 9w + 7
9w + 3 = 9w + 7
– 9w
– 9w
3≠
Subtract 9w from both sides.
7
No solution. There is no number that can be
substituted for the variable w to make the
equation true.
Course 3
Solving Equations with
11-3 Variables on Both Sides
Check It Out: Example 1C
Solve.
3w + 1 = 3w + 8
3w + 1 = 3w + 8
– 3w
– 3w
1≠
Subtract 3w from both sides.
8
No solution. There is no number that can be
substituted for the variable w to make the
equation true.
Course 3
Solving Equations with
11-3 Variables on Both Sides
To solve multi-step equations with variables on
both sides, first combine like terms and clear
fractions. Then add or subtract variable terms
to both sides so that the variable occurs on
only one side of the equation. Then use
properties of equality to isolate the variable.
Course 3
Solving Equations with
11-3 Variables on Both Sides
Additional Example 2A: Solving Multi-Step Equations
with Variables on Both Sides
Solve.
10z – 15 – 4z = 8 – 2z - 15
10z – 15 – 4z = 8 – 2z – 15
6z – 15 = –2z – 7 Combine like terms.
+ 2z
+ 2z
Add 2z to both sides.
8z – 15
+ 15
8z
8z
8
z
Course 3
=
=8
= 8
8
=1
–7
+15 Add 15 to both sides.
Divide both sides by 8.