Exercise 41 Page 92

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

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.

1/2 = 1/2c - 2

AddEqn

LHS+2=RHS+2

1/2 + 2 = 1/2c - 2 + 2

AddTerms

Add terms

1/2 + 2 = 1/2c

RearrangeEqn

Rearrange equation

1/2c = 1/2 + 2

Now we can continue to solve using the Properties of Equality.

1/2c = 1/2 + 2

MultEqn

LHS * 2=RHS* 2

2(1/2c) = 2(1/2 + 2)

Distr

Distribute 2

2(1/2c) = 2(1/2)+2(2)

MoveLeftFacToNum

a*b/c= a* b/c

2(1)/2c = 2(1)/2+2(2)

Multiply

2/2c = 2/2+4

CalcQuot

Calculate quotient

c = 1+4

AddTerms

Add terms

c = 5

The solution to the equation is c=5. We can check our solution by substituting it into the original equation.

1/2 = 1/2c - 2

Substitute

c= 5

1/2 ? = 1/2( 5) - 2

▼

Evaluate

MoveRightFacToNum

a/c* b = a* b/c

1/2 ? = 1(5)/2 - 2

CalcQuot

Calculate quotient

0.5 ? = 2.5 - 2

SubTerm

Subtract term

0.5=0.5

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

Subchapter links

Lesson Check p.91

Practice and Problem-Solving Exercises p.91-93

Standardized Test Prep p.93

Mixed Review p.93

Exercise 41 Page 92

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