Exercise 102 Page &nbsp; 127

Distribute 2

2(3x) + 2(-4) =22

6x -8 =22

LHS+8=RHS+8

6x =30

.LHS /6.=.RHS /6.

x = 5

We found that the solution is x=5. We can check our answer by substituting this value into our equation and verifying that the equality holds true.

2(3x-4)? =22

x= 5

2(3( 5)-4)? =22

▼

Evaluate left-hand side

2(15-4)? =22

SubTerm

Subtract term

2(11)? =22

22=22 ✓

Since the equality holds true, we know that x=5 is the correct answer to our equation.

b To isolate x we can start by distributing 6. That way we can see which operations need to be undone.

6(2x-5)=- (x+4)

Distribute 6

6(2x) + 6(-5) =- (x+4)

12x -30 = - (x+4)

Distribute -1

12x -30 = - x -4

LHS+x=RHS+x

13x -30 = -4

LHS+30=RHS+30

13x=26

.LHS /13.=.RHS /13.

x = 2

The solution is x=2. Let's check our answer by substituting this value into our equation and verifying that the equality holds true.

6(2x-5)? =-(x+4)

x= 2

6(2( 2)-5)? =-( 2+4)

▼

Evaluate

6(4-5)? =-(2+4)

AddSubTerms

Add and subtract terms

6(- 1)? =- 6

MultPosNeg

a(- b)=- a * b

- 6= - 6 ✓

Since we obtained a true statement, we know that x=2 is the correct answer to our equation.

c Like in previous parts, we will perform inverse operations until y is isolated.

2-(y+2)=3y

Distribute -1

2-y-2=3y

SubTerm

Subtract term

- y=3y

LHS+y=RHS+y

0 =4y

.LHS /4.=.RHS /4.

0 = y

RearrangeEqn

Rearrange equation

y=0

The solution is y=0. Let's check this answer by substituting the value into our equation.

2-(y+2)? =3y

y= 0

2-( 0+2)? =3( 0)

▼

Evaluate

ZeroPropMult

Zero Property of Multiplication

2-(0+2)? =0

Add terms

2-2? =0

SubTerm

Subtract term

0 = 0 ✓

Since we obtained a true statement, we know that y=0 is the correct answer to our equation.

d We will start by distributing the 4. That way we can proceed with using inverse operations to isolate x.

3+4(x+1)=159

Distribute 4

3+4(x) + 4(1) = 159

3+4x+4 =159

Add terms

7+4x =159

SubEqn

LHS-7=RHS-7

4x = 152

.LHS /4.=.RHS /4.

x = 38

Let's check our answer by substituting x=38 into our equation.

3+4(x+1) ? =159

x= 38

3+4( 38+1)? =159

▼

Evaluate

Add terms

3+4(39)? =159

3+156? =159