Exercise 40 Page &nbsp; 21

LHS-x=RHS-x

- 6 + 9x = 12

AddEqn

LHS+6=RHS+6

9x = 18

.LHS /9.=.RHS /9.

x=2

Let's now check this solution by substituting it into the equation. If it makes a true statement, then our solution is correct.

- 6 + 10x = x + 12

x= 2

- 6 + 10( 2)? = 2+12

Multiply

- 6 + 20? =2+12

AddTerms

Add terms

14=14

The equation is true, so x=2 is a correct solution.

b Here, we can isolate x in a similar way by performing inverse operations.

10 + 5x = 2x - 11

LHS-2x=RHS-2x

10 + 3x = -11

LHS-10=RHS-10

3x=-21

.LHS /3.=.RHS /3.

x=-7

Now we check the solution by substituting it into the equation.

10 + 5x = 2x - 11

x= -7

10 + 5( -7)? =2( -7) - 11

MultPosNeg

a(- b)=- a * b

10-35? = -14-11

SubTerm

Subtract term

-25=-25

The equation is true, so x=-7 is the solution.

c Again, we will isolate x by performing inverse operations.

- 9x = - 3x + 18

AddEqn

LHS+3x=RHS+3x

- 6x=18

.LHS /(- 6).=.RHS /(- 6).

x=-3

Let's check the solution by substituting it into the equation.

- 9x = - 3x + 18

x= - 3

- 9( -3) ? = - 3( -3) + 18

MultNegNegOnePar

- a(- b)=a* b

27? = 9 + 18

AddTerms

Add terms

27=27

The equation is true, so the solution is x=-3.

d To solve the equation, we will isolate x by performing operations.

2x - 9 = - 7x

LHS-2x=RHS-2x

-9 = -9x

.LHS /(- 9).=.RHS /(- 9).

1 =x

RearrangeEqn

Rearrange equation

x=1

Let's now check this solution by substituting it into the equation. If it makes a true statement, then our solution is correct.

2x - 9 = - 7x