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Core Connections Integrated I, 2014
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Core Connections Integrated I, 2014 View details
3. Section 3.3
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Exercise 114 Page 169

Practice makes perfect
a Notice that 4000, 8000 and 16 000 are all multiples of 4000. Therefore, by dividing both sides of the equation by 4000, we can derive an easier equation.
4000x-8000=16 000
DivEqn

.LHS /4000.=.RHS /4000.

4000x/4000-8000/4000=16 000/4000
CalcQuot

Calculate quotient

x-2=4
As we can see, x-2=4 is an equivalent equation.
b Let's solve each equation by performing inverse operations until x is isolated. If both have the same solution, they are equivalent.
4000x-8000=16 000
AddEqn

LHS+8000=RHS+8000

4000x=24 000
DivEqn

.LHS /4000.=.RHS /4000.

x=6
Let's also solve the second equation.
x-2=4
AddEqn

LHS+2=RHS+2

x=6
The second equation gives the same answer. Therefore, they have the same solution.
c Since all fractions have a denominator of 100, we can solve for x by multiplying both sides by 100.
x/100+3/100=8/100
MultEqn

LHS * 100=RHS* 100

(x/100+3/100)* 100=8/100* 100
Distr

Distribute 100

x/100* 100+3/100* 100=8/100* 100
MoveRightFacToNum

a/c* b = a* b/c

x* 100/100+3* 100/100=8* 100/100
CalcQuot

Calculate quotient

x+3=8
The easier equation is x+3=8. Let's solve this equation for x by performing inverse operations until x is isolated.
x+3=8
SubEqn

LHS-3=RHS-3

x=5
Subchapter links expand_more
arrow_right 3.3.1 Multiple Methods for Solving Equations p.169-170
114
Multiple Methods for Solving Equations 115 (Page 169)
Multiple Methods for Solving Equations 116 (Page 169)
Multiple Methods for Solving Equations 117 (Page 169)
Multiple Methods for Solving Equations 118 (Page 170)
Multiple Methods for Solving Equations 119 (Page 170)
arrow_right 3.3.2 Fraction Busters p.174-175
Fraction Busters 127 (Page 174)
Fraction Busters 128 (Page 174)
Fraction Busters 129 (Page 174)
Fraction Busters 130 (Page 175)
Fraction Busters 131 (Page 175)
arrow_right 3.3.3 Solving Exponential and Complex Equations p.178-179
Solving Exponential and Complex Equations 136 (Page 178)
137
138
Solving Exponential and Complex Equations 139 (Page 179)
Solving Exponential and Complex Equations 140 (Page 179)
Solving Exponential and Complex Equations 141 (Page 179)