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Core Connections: Course 3

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Core Connections: Course 3 View details

2. Section 9.2

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Exercise 141 Page 440

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

(x+3.5)2=16

Distribute 2

x(2)+3.5(2)=16

Multiply

2x+7=16

Now we can continue to solve using the properties of equality.

2x+7=16

LHS-7=RHS-7

2x=9

.LHS /2.=.RHS /2.

2x/2=9/2

Simplify quotient

x=9/2

Calculate quotient

x=4.5

The solution to the equation is x=4.5. We can check our solution by substituting it into the original equation. If we get a true statement after simplifying, we know our answer is correct.

(x+3.5)2=16

x= 4.5

( 4.5+3.5)2 ? = 16

▼

Simplify

Add terms

(8)2 ? = 16

Multiply

16 = 16 ✓

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

We are asked to solve the given equation. To do so, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality.

23+5x=7+2.5x

LHS-2.5x=RHS-2.5x

23+2.5x=7

LHS-23=RHS-23

2.5x=- 16

.LHS /2.5x.=.RHS /2.5x.

2.5x/2.5=- 16/2.5

Simplify quotient

x=- 16/2.5

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 16/2.5

Calculate quotient

x=- 6.4

The solution to the equation is x=- 6.4. Let's check our solution by substituting it into the original equation.

23+5x=7+2.5x

x= - 6.4

23+5( - 6.4) ? = 7+2.5( - 6.4)

▼

Simplify

a(- b)=- a * b

23+(- 32) ? = 7+(- 16)

a+(- b)=a-b

23-32 ? = 7-16

Subtract terms

- 9 = - 9 ✓

Our solution is correct because the left-hand side is equal to the right-hand side.

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. In this case, we need to start by using the Distributive Property to simplify the right-hand side of the equation.

3x+4.4=- (6.6+x)

Distribute - 1

3x+4.4=- 6.6-x

LHS+x=RHS+x

4x+4.4=- 6.6

LHS-4.4=RHS-4.4

4x=- 11

.LHS /4.=.RHS /4.

4x/4=- 11/4

Simplify quotient

x=- 11/4

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 11/4

Calculate quotient

x=- 2.75

The solution to the equation is x=- 2.75. Let's check our solution by substituting it into the original equation.

3x+4.4=- (6.6+x)

x= - 2.75

3( - 2.75)+4.4 ? = - [6.6+( - 2.75)]

▼

Simplify

a+(- b)=a-b

3(- 2.75)+4.4 ? = - (6.6-2.75)

Subtract term

3(- 2.75)+4.4 ? = - 3.85

Multiply

- 8.25+4.4 ? = - 3.85

Add terms

- 3.85 = - 3.85 ✓

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

Subchapter links

9.2.1 Side Lengths and Triangles p.413-415

9.2.2 Pythagorean Theorem p.420

9.2.3 Understanding Square Root p.425-427

9.2.4 Real Numbers p.432-434

9.2.5 Applications of the Pythagorean Theorem p.437

9.2.6 Pythagorean Theorem in Three Dimensions p.440-441

9.2.7 Pythagorean Theorem Proofs p.444-445