Algebra 1 Ch 3.4 – Solving Equations with Variables on Both Sides.
Solving Equations with Variables on Both Sides 11-3 Learn to solve equations with variables on both...
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Solving Equations with Variables on Both Sides 11-3 Learn to solve equations with variables on both sides of the equal sign.
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Transcript of Solving Equations with Variables on Both Sides 11-3 Learn to solve equations with variables on both...
Solving Equations with Variables on Both Sides11-3
Learn to solve equations with variables on both sides of the equal sign.
Solving Equations with Variables on Both Sides11-3
Solve.
4x + 6 = x
Example 1:
4x + 6 = x– 4x – 4x
6 = –3x
Subtract 4x from both sides.
Divide both sides by –3.
–2 = x
6–3
–3x–3=
Solving Equations with Variables on Both Sides11-3
Solve.
9b – 6 = 5b + 18
Example 2:
9b – 6 = 5b + 18– 5b – 5b
4b – 6 = 18
4b 4
24 4 =
Subtract 5b from both sides.
Divide both sides by 4.
b = 6
+ 6 + 6
4b = 24Add 6 to both sides.
Solving Equations with Variables on Both Sides11-3
Solve.
9w + 3 = 9w + 7
Example 3:
3 ≠ 7
9w + 3 = 9w + 7
– 9w – 9w Subtract 9w from both sides.
No solution. There is no number that can be substituted for the variable w to make the equation true.
Solving Equations with Variables on Both Sides11-3
If the variables in an equation are eliminated and the resulting statement is false, the equation has no solution.
Helpful Hint
Solving Equations with Variables on Both Sides11-3
Solve.
3b – 2 = 2b + 123b – 2 = 2b + 12
– 2b – 2b
b – 2 = 12
Subtract 2b from both sides.
+ 2 + 2
b = 14Add 2 to both sides.
Practice- Example 5:
Solving Equations with Variables on Both Sides11-3
Solve.
3w + 1 = 3w + 8
1 ≠ 8
3w + 1 = 3w + 8
– 3w – 3w Subtract 3w from both sides.
No solution. There is no number that can be substituted for the variable w to make the equation true.
Practice- Example 6:
Solving Equations with Variables on Both Sides11-3
Solve.
10z – 15 – 4z = 8 – 2z - 15
Challenge Problem
10z – 15 – 4z = 8 – 2z – 15
+ 15 +15
6z – 15 = –2z – 7 Combine like terms.+ 2z + 2z Add 2z to both sides.
8z – 15 = – 7
8z = 8
z = 1
Add 15 to both sides.
Divide both sides by 8.8z 88 8=
Solving Equations with Variables on Both Sides11-3
Business Application
Daisy’s Flowers sell a rose bouquet for $39.95 plus $2.95 for every rose. A competing florist sells a similar bouquet for $26.00 plus $4.50 for every rose. Find the number of roses that would make both florists’ bouquets cost the same price.
