Exercise 17 Page 14

Practice makes perfect

a By using the Division Property of Equality we can solve for x.

-11x=77

.LHS /(-11).=.RHS /(-11).

x=-7

To check our solution, we have to substitute it into the original equation and simplify. If the left-hand side and right-hand side are equal, the solution is correct.

-11x=77

Substitute

x= - 7

-11( -7)? =77

Multiply

77=77 ✓

The solution is correct.

b To solve the equation, we should start by gathering all variable terms on one side of the equation and all constant terms on the other side. We can then use the Subtraction Property of Equality and Division Property of Equality to solve for c.

5c+1=7c-8

SubEqn

LHS-1=RHS-1

5c=7c-9

SubEqn

LHS-7c=RHS-7c

-2c=-9

DivEqn

.LHS /(- 2).=.RHS /(- 2).

c=-9/-2

DivNegNeg

- a/- b=a/b

c=9/2

To check our solution, we have to substitute it into the original equation and simplify. If the left-hand side and right-hand side are equal, the solution is correct.

5c+1=7c-8

Substitute

c= 9/2

5( 9/2)+1? =7( 9/2)-8

▼

Evaluate

MoveLeftFacToNum

a*b/c= a* b/c

45/2+1? =63/2-8

CalcQuot

Calculate quotient

22.5+1? =31.5-8

AddSubTerms

Add and subtract terms

23.5=23.5 ✓

The solution is correct.

c By using the Multiplication Property of Equality we can solve for x.

x/8=2

MultEqn

LHS * 8=RHS* 8

x=16

To check our solution, we have to substitute it into the original equation and simplify. If the left-hand side and right-hand side are equal, the solution is correct.

x/8=2

Substitute

x= 16

16/8? =2

CalcQuot

Calculate quotient

2=2 ✓

The solution is correct.

d Begin by gathering all variable terms on one side of the equation and all constant terms on the other side. Then use the Subtraction Property of Equality and Division Property of Equality to solve for x.

-12=3k+9

SubEqn

LHS-9=RHS-9

-21=3k

RearrangeEqn

Rearrange equation

3k=-21

DivEqn

.LHS /3.=.RHS /3.

k=-7

To check our solution, we have to substitute it into the original equation and simplify. If the left-hand side and right-hand side are equal, the solution is correct.

-12=3k+9

Substitute

k= - 7

-12? =3( - 7)+9

Multiply

-12? =- 21+9

AddTerms

Add terms

-12=- 12 ✓

The solution is correct.