Exercise 58 Page 566

Practice makes perfect

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

4/5x-2=7

AddEqn

LHS+2=RHS+2

4/5x=9

MultEqn

LHS * 5=RHS* 5

4x=45

DivEqn

.LHS /4.=.RHS /4.

x=11.25

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

3x^2=300

DivEqn

.LHS /3.=.RHS /3.

x^2=100

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 10

c 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.

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

MultEqn

LHS * 2=RHS* 2

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

MultEqn

LHS * 3=RHS* 3

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

Distr

Distribute 2 & 3

12x-3=2x+10

SubEqn

LHS-2x=RHS-2x

10x-3=10

AddEqn

LHS+3=RHS+3

10x=13

DivEqn

.LHS /10.=.RHS /10.

x=1.3

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

x=- b± sqrt(b^2-4ac)/2a

a= 1, b= - 4, c= 6

x=- ( - 4)± sqrt(( - 4)^2-4( 1)( 6))/2( 1)

NegNeg

- (- a)=a

x=4 ± sqrt((- 4)^2-4(1)(6))/2(1)

NegBaseToPosPow

(- a)^2 = a^2

x=4 ± sqrt(4^2-4(1)(6))/2(1)

CalcPow

Calculate power

x=4 ± sqrt(16-4(1)(6))/2(1)

Multiply

x=4 ± sqrt(16-24)/2

SubTerm

Subtract term

x=- 8± sqrt(- 8)/2

Since we cannot take the square root of a negative number, we know that there are no real solutions to this equation.

Hints

Check the answer

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