Exercise 3 Page &nbsp; 48

a= 3

3(x- 3)=3x-6

▼

Solve for x

Distribute 3

3x-9=3x-6

LHS-3x=RHS-3x

-9 ≠ -6

We have reached a contradiction, which means this equation has no solution. Therefore, the number of solutions N is less than 1.

When a=3, N < 1.

b We can follow the same steps as in the previous exercise. Let's substitute a= - 3 and try to solve the equation.

3(x-a)=3x-6

a= -3

3(x-( -3))=3x-6

▼

Solve for x

SubNeg

a-(- b)=a+b

3(x+3)=3x-6

Distribute 3

3x+9=3x-6

LHS-3x=RHS-3x

9 ≠ -6

Solving the equation resulted in a contradiction, so this equation has no solution. Therefore, the number of solutions N is less than 1.

When a=- 3, N < 1.

c Let's substitute a= 2 and try to solve the equation.

3(x-a)=3x-6

a= 2

3(x- 2)=3x-6

▼

Solve for x

Distribute 3

3x-6=3x-6

LHS-3x=RHS-3x

-6= -6

We have reached an identity, which is always true no matter the value of x. This equation has infinitely many solutions and therefore, the number of solutions N is more than 1.

When a=2, N > 1.

d We can do the same thing as in the previous exercises. We will substitute a= - 2 and try to solve the equation.

3(x-a)=3x-6

a= -2

3(x-( -2))=3x-6

▼

Solve for x

SubNeg

a-(- b)=a+b

3(x+2)=3x-6

Distribute 3

3x+6=3x-6

LHS-3x=RHS-3x

6 ≠ -6

We got a contradiction, so this equation has no solution. Therefore, the number of solutions N is less than 1.

When a=- 2, N < 1.

e Let's substitute a= x and try to solve the equation.

3(x-a)=3x-6

a= x

3(x- x)=3x-6

▼

Solve for x

SubTerm

Subtract term

3*0=3x-6

ZeroPropMult

Zero Property of Multiplication

0=3x-6

AddEqn

LHS+6=RHS+6

6=3x

DivEqn

.LHS /3.=.RHS /3.

2=x

RearrangeEqn

Rearrange equation

x=2

We found that x=2 is the solution to this equation, so the number of solutions N is 1.

When a=x, N = 1.

f We can do the same thing as in the previous exercises. Substitute a= - x and try to solve the equation.

3(x-a)=3x-6

a= - x

3(x-( - x))=3x-6

▼

Solve for x

SubNeg

a-(- b)=a+b

3(x+x)=3x-6

AddTerms

Add terms

3(2x)=3x-6

Multiply

6x=3x-6