Exercise 69 Page 572

Practice makes perfect

a By multiplying both sides of the equation by both denominators, we can eliminate the fractions and then proceed to solve the equation by performing inverse operations.

8-x/x=3/2

MultEqn

LHS * x=RHS* x

8-x=3/2* x

MultEqn

LHS * 2=RHS* 2

2(8-x)=3x

Distr

Distribute 2

16-2x=3x

AddEqn

LHS+2x=RHS+2x

16=5x

DivEqn

.LHS /5.=.RHS /5.

16/5=x

RearrangeEqn

Rearrange equation

x=16/5

b Before we can solve this equation we have to distribute the factor outside of the parentheses on the left-hand side. After that we can perform inverse operations until x is isolated.

- 2(5x-1)-3=- 10 x

Distr

Distribute - 2

- 10 x+2-3=- 10 x

SubTerm

Subtract term

- 10 x-1=- 10 x

AddEqn

LHS+10x=RHS+10x

- 1≠ 0

This equation has no real solutions.

c To solve this equation we will use the Quadratic Formula.

x=- b± sqrt(b^2-4ac)/2a

a= 1, b= 8, c= - 33

x=- 8± sqrt(8^2-4( 1)( - 33))/2( 1)

CalcPow

Calculate power

x=- 8± sqrt(64-4(1)(- 33))/2(1)

Multiply

x=- 8± sqrt(64+132)/2

AddTerms

Add terms

x=- 8± sqrt(196)/2

CalcRoot

Calculate root

x=- 8± 14/2

Finally, to find the solutions we have to split the fraction into the positive and negative cases. Positive:& - 8 + 14/2= 3 [0.5em] Negative:& - 8 - 14/2=- 11 The equations solutions are x=3 and x=- 11.

d Here we will perform inverse operations until we have isolated the variable.

2/3x-12=180

AddEqn

LHS+12=RHS+12

2/3x=192

MultEqn

LHS * 3=RHS* 3

2x=576

DivEqn

.LHS /2.=.RHS /2.

x=288

Hints

Check the answer

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