Equivalent Equations

Equivalent Equations

Equivalent Equations have the same solution

Multiple Choice

True or False?

4 + 5 = 2 + 7

• True

• False

Multiple Choice

True or False?

9 + 4 = 5 + 7

• True

• False

Multiple Choice

Are these equivalent? 

 $\frac{18}{2}=\frac{27}{3}$  

• True

• False

Multiple Choice

Are these equivalent?

 $5\times8=4\times11$  

• True

• False

Write this down!

Write this down

Reciprocal = flipped fraction; Write this down

The reciprocal of  $\frac{2}{1}$   is  $\frac{1}{2}$  

The reciprocal of  $\frac{2}{5}$  is  $\frac{5}{2}$  
**We use "reciprocals" to multiply each side to eliminate a fraction**
For example: Solve for x: 
 $\frac{3}{4}x=8$       the reciprocal is  $\frac{4}{3}$  
 $\frac{4}{3}\left(\frac{3}{4}x\right)=8\left(\frac{4}{3}\right)$  the fractions on the L eliminate & multiply on R
 $x=\frac{32}{3}=10.67$  

Multiple Choice

Find the reciprocal1/8

• 8
• 1/8

Multiple Choice

What is the recriprocal of 5

• 5/1
• 1/5

Multiple Choice

What is the recriprocal of 4/5

• 4/5
• 5/4
• 5/1
• 1/5

Fill in the Blanks

 $\frac{1}{4}x=8$  

Which value of x makes this statement true? Multiply both sides by the reciprocal

Fill in the Blanks

 $x+3=5$  

What value of x makes this statement true?

Fill in the Blanks

What value of x makes this statement true?

5x=35

Fill in the Blanks

 $3x+2=11$  

What value of "x" makes this statement true?

Multiple Choice

What value of "m" makes this statement true?

13= 5m -2

• -3

• 2

• 3

• -2

Distributive Property

Multiplying the number outside the () to each number inside the () will produce the same equation

3(x+2) = 6 + 3x

3x + 6 = 3x + 6

Multiple Choice

2(c - 8)

• 2c - 16
• 2c + 16
• 2c - 8
• c - 16

Multiple Choice

-4(k - 7)

• -4k + 28
• -4k - 28
• 4k + 28
• 4k - 28

Multiple Choice

 $-2\left(2x+4\right)=4x+8$  

Are these equations equivalent?

• Yes

• No

Multiple Choice

Are these equations Equivalent?

3(4y + 3) = 12y + 6

• Equivalent

• Not Equivalent