ESSENTIAL SKILLS:SOLVE EQUATIONS WITH THE VARIABLE ON EACH SIDE

SOLVE EQUATIONS INVOLVING GROUPING SYMBOLS

2-4: Solving Equations with Variables on Both Sides

2-4: Equations with variables on both sides

Example 1: Solve an Equation with Variables on both sides

Solve 8 + 5c = 7c – 2. Check your solution. 8 + 5c = 7c – 2 Original Equation - 7c -7c Subtract 7c from each side 8 – 2c = -2 Simplify -8 -8 Subtract 8 from each side -2c = -10 Simplify ÷-2 ÷-2 Divide each side by -2 c = 5

1) Solve 9f – 6 = 3f + 7

1 2 3 4

8% 4%

88%

0%

1. 1/3

2. 1/12

3. 13/6

4. 2

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2-4: Equations with variables on both sides

Example 2: Solve an Equation with Grouping Symbols

Solve 1/3(18 + 12q) = 6(2q – 7) 1/3(18 + 12q) = 6(2q – 7) Original Equation 6 + 4q = 12q – 42 Distribute - 12q -12q Subtract 12q from each side 6 – 8q = -42 Simplify -6 -6 Subtract 6 from each side -8q = -48 Simplify ÷-8 ÷-8 Divide each side by -8 q = 6

2) Solve 6(3r – 4) = 3/8(46r + 8)

1 2 3 4

0%

88%

8%4%

1. 382. 283. 104. 36

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2-4: Equations with variables on both sides

Example 3A: Special CasesSolve 8(5c – 2) = 10(32 + 4c)

8(5c – 2) = 10(32 + 4c) Original Equation 40c – 16 = 320 + 40c Distribute -40c -40c Subtract 40c from

each side -16 = 320 Simplify

This statement is false, so there is no solution

2-4: Equations with variables on both sides

Example 3B: Special CasesSolve 4(t + 20) = 1/5(20t + 400)

4(t + 20) = 1/5(20t + 400) Original Equation 4t + 80 = 4t + 80 Distribute

This statement is true, so all real numbers are solutions

3) Solve 2(4a + 8) = 3(8a/3 – 10)

1 2 3 4

0%

92%

4%4%

1. 1/3

2. 23. All real numbers4. No solution

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4) Solve 1/7(21c – 56) = 3(c – 8/3)

1 2 3 4

0%8%

88%

4%

1. 1/3

2. 03. All real numbers4. No solution

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2-4: Equations with variables on both sides

In summary Step 1: Simplify the expression on each side. Use the

Distributive Property if necessary. Step 2: Use the Addition and/or Subtraction

Properties of Equality to get the variables on one side (preferably the left) and numbers without variables on the other side. Simplify.

Step 3: Use the Multiplication or Division Property of Equality to solve.

Candy!!!

4 Bryant Montoya4 Grace Pool4 Steven Herrera-

Jimenez4 Romeo Tramel4 Zachary Grant

2-4: Equations with variables on both sides

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