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Core Connections Geometry, 2013 View details

2. Section 1.2

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Exercise 57 Page 33

Practice makes perfect

a To solve the equation we first have to simplify the left-hand side. Note that all variables on the left-hand side are of the same kind and can therefore be combined to a single variable term.

5x-2x+x=15

AddSubTerms

Add and subtract terms

4x=15

DivEqn

.LHS /4.=.RHS /4.

4x/4=15/4

CalcQuot

Calculate quotient

x=3.75

b To solve for x, first want to have all x-terms on the same side. Remember inverse operations and the Properties of Equality.

3x-2-x=7-x

AddEqn

LHS+x=RHS+x

3x-2=7

AddEqn

LHS+2=RHS+2

3x=9

DivEqn

.LHS /3.=.RHS /3.

x=3

c Here, we first have to distribute 3 over the parentheses. After that we want to have all x-terms on one side. We do this with inverse operations and the Properties of Equality.

3(x-1)=2x-3+3x

Distr

Distribute 3

3x-3=2x-3+3x

SubEqn

LHS-3x=RHS-3x

-3=2x-3

AddEqn

LHS+3=RHS+3

0=2x

RearrangeEqn

Rearrange equation

2x=0

DivEqn

.LHS /2.=.RHS /2.

x=0

d To solve this equation, we once again have to distribute 3 over the parentheses. We also have to distribute 5 on the right-hand side.

3(2-x)=5(2x-7)+2

Distr

Distribute 3

6-3x=5(2x-7)+2

Distr

Distribute 5

6-3x=10x-35+2

Now, we want to have all x-terms on one side and all constants on the other side. We do this with inverse operations and the Properties of Equality.

6-3x=10x-35+2

AddTerms

Add terms

6-3x=10x-33

SubEqn

LHS-6=RHS-6

-3x=10x-39

SubEqn

LHS-10x=RHS-10x

-13x=-39

DivEqn

.LHS /(-13).=.RHS /(-13).

x=-39/-13

DivNegNeg

- a/- b=a/b

x=39/13

CalcQuot

Calculate quotient

x=3

e Notice that there is division on both sides of the equality sign. We will solve the equation by multiplying each side by the least common denominator, 57(5x), to clear denominators.

26/57=849/5x

MultEqn

LHS * 57(5x)=RHS* 57(5x)

26/57* 57(5x) = 849/5x * 57(5x)

▼

Multiply

MoveRightFacToNum

a/c* b = a* b/c

26(57)(5x)/57 = 849(57)(5x)/5x

CancelCommonFac

Cancel out common factors

26(57)(5x)/57 = 849(57)(5x)/5x

SimpQuot

Simplify quotient

26(5x) = 849(57)

Multiply

130x = 48 393

DivEqn

.LHS /130.=.RHS /130.

x= 372.25384...

RoundDec

Round to 2 decimal place(s)

x≈ 372.25

f Similarly as in Part E, we notice that there is division on both sides of the equation. This means we can solve the equation by multiplying each side by the least common denominator, 3(2), to clear denominators.

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

▼

Multiply

MultEqn

LHS * 3(2)=RHS* 3(2)

4x+1/3* 3(2)=x-5/2* 3(2)

MoveRightFacToNum

a/c* b = a* b/c

(4x+1)(3)(2)/3 = (x-5)(3)(2)/2

CancelCommonFac

Cancel out common factors

(4x+1)(3)(2)/3 = (x-5)(3)(2)/2