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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

3. Solving Equations

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Exercise 58 Page 23

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

z=32/5

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side, using the Properties of Equality. Let's start using the Addition and Subtraction Properties of Equality.

3/4z-1/3=2/3z+1/5

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LHS+1/3=RHS+1/3

LHS+1/3=RHS+1/3

3/4z-1/3+1/3=2/3z+1/5+1/3

a/b=a * 3/b * 3

3/4z-1/3+1/3=2/3z+3/15+1/3

a/b=a * 5/b * 5

3/4z-1/3+1/3=2/3z+3/15+5/15

Add fractions

3/4z=2/3z+8/15

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LHS-2/3z=RHS-2/3z

LHS-2/3z=RHS-2/3z

3/4z-2/3x=2/3z+8/15-2/3z

a/b=a * 3/b * 3

9/12z-2/3x=2/3z+8/15-2/3z

a/b=a * 4/b * 4

9/12z-8/12x=2/3z+8/15-2/3z

Subtract fractions

1/12z=8/15

Now we can continue to solve using the Multiplication Property of Equality.

1/12z=8/15

MoveRightFacToNum

a/c* b = a* b/c

z/12=8/15

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LHS * 12=RHS* 12

LHS * 12=RHS* 12

12*z/12=12*8/15

DenomMultFracToNumber

12 * a/12= a

z=12*8/15

MoveLeftFacToNum

a*b/c= a* b/c

z=12*8/15

a/b=.a /3./.b /3.

z=4*8/5

Multiply

z=32/5

The solution to the equation is z= 325. We can check our solution by substituting it into the original equation.

3/4z-1/3=2/3z+1/5

z= 32/5

3/4( 32/5)-1/3 ? = 2/3( 32/5)+1/5

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Simplify

Multiply fractions

3(32)/4(5)-1/3? = 2(32)/3(5)+1/5

a/b=.a /4./.b /4.

3(8)/5-1/3? = 2(32)/3(5)+1/5

Multiply

24/5-1/3? =64/15+1/5

a/b=a * 3/b * 3

72/15-1/3? =64/15+3/15

a/b=a * 5/b * 5

72/15-5/15? =64/15+3/15

Add and subtract fractions

67/15=67/15

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Check Your Understanding p.22

Practice and Problem Solving p.22-24

H.O.T. Problems p.24

Standardized Test Practice p.25

Spiral Review p.25

Skills Review p.25