Exercise 33 Page 378

Practice makes perfect

a To solve an equation using the Properties of Equality, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

2x-10=0

AddEqn

LHS+10=RHS+10

2x=10

DivEqn

.LHS /2.=.RHS /2.

x=5

The solution to the equation is x=5. We can check our solution by substituting it into the original equation.

2x-10=0

Substitute

x= 5

2( 5)-10? =0

▼

Simplify

Multiply

10-10 ? = 0

SubTerm

Subtract term

0=0

Since the left-hand side is equal to the right-hand side, our solution is correct.

b To solve an equation using the Properties of Equality, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

x+6=0

SubEqn

LHS-6=RHS-6

x=- 6

The solution to the equation is x=- 6. We can check our solution by substituting it into the original equation.

x+6=0

Substitute

x= - 6

- 6+6 ? = 0

AddTerms

Add terms

0=0

Since the left-hand side is equal to the right-hand side, our solution is correct.

c To solve the given equation we will use the Zero Product Property.

(2x-10)(x+6)=0

ZeroProdProp

Use the Zero Product Property

lc2x-10=0 & (I) x+6=0 & (II)

AddEqn

(I): LHS+10=RHS+10

l2x=10 x+6=0

DivEqn

(I): .LHS /2.=.RHS /2.

lx=5 x+6=0

SubEqn

(II): LHS-6=RHS-6

lx_1=5 x_2=- 6

The solutions for our equation are 5 and - 6. To check our answers, we will substitute them for x in the given equation. Let's start with x=5.

(2x-10)(x+6)=0

Substitute

x= 5

(2( 5)-10)( 5+6)? =0

▼

Simplify

Multiply

(10-10)(5+6)? =0

AddSubTerms

Add and subtract terms

(0)(11)? =0

ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that x=5 is a solution of the equation. Let's now check x=- 6.

(2x-10)(x+6)=0

Substitute

x= - 6

(2( - 6)-10)( - 6+6)? =0

▼

Simplify

MultPosNeg

a(- b)=- a * b

(- 12-10)(- 6+6)? =0

AddSubTerms

Add and subtract terms

(- 22)(0)? =0

IdPropMult

Identity Property of Multiplication

0=0 ✓

This is also a true statement, so we know that x=- 6 is a solution of the equation.

d To solve an equation using the Properties of Equality, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

4x+1=0

SubEqn

LHS-1=RHS-1

4x=- 1

DivEqn

.LHS /4.=.RHS /4.

x=- 1/4

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 1/4

The solution to the equation is x=- 14. We can check our solution by substituting it into the original equation.

4x+1=0

Substitute

x= - 1/4

4 ( - 1/4)+1 ? = 0

▼

Simplify

MultPosNeg

a(- b)=- a * b

- 4 (1/4)+1 ? = 0

DenomMultFracToNumber

4 * a/4= a

- 1+1 ? = 0

AddTerms

Add terms

0=0

Since the left-hand side is equal to the right-hand side, our solution is correct.

e To solve an equation using the Properties of Equality, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

x-8=0

AddEqn

LHS+8=RHS+8

x=8

The solution to the equation is x=8. We can check our solution by substituting it into the original equation.

x-8=0

Substitute

x= 8

8-8 ? = 0

SubTerm

Subtract term

0=0