ALGEBRA 1 LESSON 2-4 Equations with Variables on Both Sides Simplify. (For help, go to Lessons 1-7 and 2-3.) 1.
Download ReportTranscript ALGEBRA 1 LESSON 2-4 Equations with Variables on Both Sides Simplify. (For help, go to Lessons 1-7 and 2-3.) 1.
Slide 1
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Sides
Simplify.
(For help, go to Lessons 1-7 and 2-3.)
1. 6x – 2x
2. 2x – 6x
3. 5x – 5x
4. –5x + 5x
Solve each equation.
5. 4x + 3 = –5
6. –x + 7 = 12
7. 2t – 8t + 1 = 43
8. 0 = –7n + 4 – 5n
2-4
Slide 2
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Solutions
Sides
1.
6x – 2x = (6 – 2)x = 4x
2.
3.
5x – 5x = (5 – 5)x = 0x = 0
4. –5x + 5x = (–5 + 5)x = 0x = 0
5.
4x + 3 = –5
4x = –8
x = –2
7. 2t – 8t + 1 =
–6t + 1 =
–6t =
t=
6.
43
43
42
–7
8.
2-4
2x – 6x = (2 – 6)x = –4x
–x + 7 = 12
–x = 5
x = –5
0
0
12n
n
=
=
=
=
–7n + 4 – 5n
–12n + 4
4
1
3
Slide 3
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
The measure ofSides
an angle is (5x – 3)°. Its vertical angle has
a measure of (2x + 12)°. Find the value of x.
5x – 3 = 2x + 12
Vertical angles are congruent.
5x – 3 – 2x = 2x + 12 – 2x
Subtract 2x from each side.
3x – 3 = 12
Combine like terms.
3x – 3 + 3 = 12 + 3
Add 3 to each side.
3x = 15
Simplify.
3x = 15
3
3
Divide each side by 3.
x = 5
Simplify.
2-4
Slide 4
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
You can buy a skateboard
for $60 from a friend and rent the
Sides
safety equipment for $1.50 per hour. Or you can rent all items you
need for $5.50 per hour. How many hours must you use a
skateboard to justify buying your friend’s skateboard?
Relate: cost of plus equipment equals skateboard and equipment
friend’s
rental
rental
skateboard
Define: let h = the number of hours you must skateboard
Write:
60
+
1.5 h
=
2-4
5.5 h
Slide 5
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Sides
(continued)
60 + 1.5h = 5.5h
60 + 1.5h – 1.5h = 5.5h – 1.5h
Subtract 1.5h from each side.
60 = 4h
Combine like terms.
60
4h
=
4
4
Divide each side by 4.
15 = h
Simplify.
You must use your skateboard for more than 15 hours to justify buying the
skateboard.
2-4
Slide 6
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Solve each equation.
Sides
–6z + 8 = z + 10 – 7z
–6z + 8 = z + 10 – 7z
–6z + 8 = –6z + 10
Combine like terms.
–6z + 8 + 6z = –6z + 10 + 6z Add 6z to each side.
8 = 10
Not true for any value of z!
This equation has no solution
b.
4 – 4y = –2(2y – 2)
4 – 4y = –2(2y – 2)
4 – 4y = –4y + 4
Use the Distributive Property.
4 – 4y + 4y = –4y + 4 + 4y
Add 4y to each side.
4 = 4
Always true!
The equation is true for every value of y, so the equation is an identity.
a.
2-4
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Sides
Simplify.
(For help, go to Lessons 1-7 and 2-3.)
1. 6x – 2x
2. 2x – 6x
3. 5x – 5x
4. –5x + 5x
Solve each equation.
5. 4x + 3 = –5
6. –x + 7 = 12
7. 2t – 8t + 1 = 43
8. 0 = –7n + 4 – 5n
2-4
Slide 2
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Solutions
Sides
1.
6x – 2x = (6 – 2)x = 4x
2.
3.
5x – 5x = (5 – 5)x = 0x = 0
4. –5x + 5x = (–5 + 5)x = 0x = 0
5.
4x + 3 = –5
4x = –8
x = –2
7. 2t – 8t + 1 =
–6t + 1 =
–6t =
t=
6.
43
43
42
–7
8.
2-4
2x – 6x = (2 – 6)x = –4x
–x + 7 = 12
–x = 5
x = –5
0
0
12n
n
=
=
=
=
–7n + 4 – 5n
–12n + 4
4
1
3
Slide 3
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
The measure ofSides
an angle is (5x – 3)°. Its vertical angle has
a measure of (2x + 12)°. Find the value of x.
5x – 3 = 2x + 12
Vertical angles are congruent.
5x – 3 – 2x = 2x + 12 – 2x
Subtract 2x from each side.
3x – 3 = 12
Combine like terms.
3x – 3 + 3 = 12 + 3
Add 3 to each side.
3x = 15
Simplify.
3x = 15
3
3
Divide each side by 3.
x = 5
Simplify.
2-4
Slide 4
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
You can buy a skateboard
for $60 from a friend and rent the
Sides
safety equipment for $1.50 per hour. Or you can rent all items you
need for $5.50 per hour. How many hours must you use a
skateboard to justify buying your friend’s skateboard?
Relate: cost of plus equipment equals skateboard and equipment
friend’s
rental
rental
skateboard
Define: let h = the number of hours you must skateboard
Write:
60
+
1.5 h
=
2-4
5.5 h
Slide 5
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Sides
(continued)
60 + 1.5h = 5.5h
60 + 1.5h – 1.5h = 5.5h – 1.5h
Subtract 1.5h from each side.
60 = 4h
Combine like terms.
60
4h
=
4
4
Divide each side by 4.
15 = h
Simplify.
You must use your skateboard for more than 15 hours to justify buying the
skateboard.
2-4
Slide 6
ALGEBRA 1 LESSON 2-4
Equations with Variables on Both
Solve each equation.
Sides
–6z + 8 = z + 10 – 7z
–6z + 8 = z + 10 – 7z
–6z + 8 = –6z + 10
Combine like terms.
–6z + 8 + 6z = –6z + 10 + 6z Add 6z to each side.
8 = 10
Not true for any value of z!
This equation has no solution
b.
4 – 4y = –2(2y – 2)
4 – 4y = –2(2y – 2)
4 – 4y = –4y + 4
Use the Distributive Property.
4 – 4y + 4y = –4y + 4 + 4y
Add 4y to each side.
4 = 4
Always true!
The equation is true for every value of y, so the equation is an identity.
a.
2-4