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Algebra 1

1.6.2 Expressing Relationships as Equations

Algebra 11.6.2 Expressing Relationships as Equations

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Activity

In 1 - 3:

Write as many equations as possible that could represent the relationship between the ages of the two children in each family described. Be prepared to explain what each part of your equation represents.
1.

In Family A, the youngest child is 7 years younger than the oldest, who is 18.

2.

In Family B, the middle child is 5 years older than the youngest child.

3.

Tyler thinks that the relationship between the ages of the children in Family B can be described with 2m2y=102m2y=10, where mm is the age of the middle child and yy is the age of the youngest. Describe how Tyler came up with this equation.

4.

Select three equations that are equivalent to 3a+6=153a+6=15.

  • a + 3 = 12 a+3=12
  • 3 a = 9 3a=9
  • 1 3 a = 1 1 3 a=1
  • a + 2 = 5 a+2=5
5.

Explain your reasoning for the equivalent equations in number 4.

Are you ready for more?

Extending Your Thinking

Here is a puzzle:

  • m+m=Nm+m=N
  • N+N=pN+N=p
  • m+p=Qm+p=Q
  • p+Q=?p+Q=?

Write two expressions that are equivalent to p+Qp+Q.

Self Check

Which equation is equivalent to 3 x 6 = 18 ?
  1. 3 x + 12 = 0
  2. x 2 = 18
  3. 3 x = 12
  4. 3 x = 24

Additional Resources

Finding Equivalent Equations

Equivalent equations are equations that have the same solutions. They are often found by using inverse operations or by multiplying each term in the equation by the same value.

Example

Write three equivalent equations to 4x2=84x2=8 using one of three strategies.

  • Using an inverse operation
  • Using division
  • Using multiplication

Using an inverse operation:
An equivalent equation can be determined by adding 2 to both sides.

4x2=84x2=8
4x2+2=8+24x2+2=8+2
4x=104x=10
(4x2=8)(4x2=8) and (4x=10)(4x=10) are equivalent.

Using division:
An equivalent equation can be determined by dividing by 2 (or multiplying by 1212).

4x2=84x2=8
(12)(4x2)=(12)(8)(12)(4x2)=(12)(8)
2x1=42x1=4

(4x2=8)(4x2=8) and (2x1=4)(2x1=4) are equivalent.

Using multiplication:
An equivalent equation can be determined by multiplying the same number to both sides.

What is the equivalent equation if you multiply each term in the equation 4x2=84x2=8 by 3?

Try it

Try It: Finding Equivalent Equations

1.

Determine the equivalent equation if you subtract 5 from each side of the equation, 3x+5=153x+5=15

2.

Explain how (3x=10)(3x=10) is related to (x=103)(x=103)

3.

Multiply every term by the same number to determine an equivalent equation to 3x+5=153x+5=15.

4.

Is (3x+5=15)(3x+5=15) equivalent to (6x+15=60)(6x+15=60)

5.

Explain your reasoning for your answer to number 4 and whether the equations (3x+5=15)(3x+5=15) and (6x+15=60)(6x+15=60) are equivalent.

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