Equivalent Equations

Multiple Select

Select all the equations that have the same solution as  $$2x-5=15$$  .

• $$2x=10$$  

• $$2x=20$$  

• $$2\left(x-5\right)=15$$  

• $$2x-20=0$$  

• $$4x-10=30$$  

Multiple Choice

Which equation is equivalent to the equation $$5x+30=45$$  ?

• $$35x=45$$  

• $$5x=75$$  

• $$5\left(x+30\right)=45$$  

• $$5\left(x+6\right)=45$$  

Multiple Choice

The entrepreneurship club is ordering potted plants for all 36 of its sponsors. One store charges $8.50 for each plant plus a delivery fee of $20. The equation  $$320=x+7.50\left(36\right)\$$  represents the cost of ordering potted plants at a second store.

What does the x represent in this situation?

• The cost for each potted plant at the second store

• The delivery fee at the second store

• The total cost of ordering potted plants at the second store

• The number of sponsors of the entrepreneurship club

Multiple Choice

Kiran says that a solution to the equation  $$x+4=20\$$  must also be a solution to the equation  $$5\left(x+4\right)=100$$  .  Select the most convincing reason why this is true.

• It just is.

• If you multiply both sides of  $$x+4=20$$  by 5, you get  $$5\left(x+4\right)=100$$  .

• Because  $$5x+4=100$$  .

• The equations are just equivalent.

Fill in the Blanks

Is 0 a solution to  $2x+10=4x+10$  ?  Explain.

Multiple Select

Select all equations that are equivalent to

$$3\left(x+6\right)=4x+7$$  .

• $$3\left(x+6\right)=4x+7$$  

• $$3x=4x+7$$  

• $$3x+18=4x+7$$  

• $$18=x+7$$  

Multiple Choice

Which equation is equivalent to the equation $$5x+30=45$$  ?

• $$35x=45$$  

• $$5x=75$$  

• $$5\left(x+30\right)=45$$  

• $$5\left(x+6\right)=45$$  

Multiple Choice

Diegos's age is n is 5 more than 2 times his sister's age s. This situation is represented by the equation d=2s+5. Which equation is equivalent to the equation d=2s+5?

• $$d=2\left(s+5\right)$$

• $$d-5=2s$$

• $$d-2=s+5$$

• $$\frac{d}{2}=s+5$$

Dropdown

Given the equation 5x + 15 = 2, if you ​

Select answer

both sides by ​

Select answer

you get 10x + 30 = 4 as an equivalent equation.

Drag and Drop

Given the equation 4x - 12 = -80, what was done to both sides to get the following equations?

2x - 6 = -40 ​

Placeholder

12x - 36 = -240 ​

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4x - 15 = -83 ​

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4x - 9 = -77 ​

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Drag these tiles and drop them in the correct blank above

Divide by 2

Multiply by 3

Subtract 3

Add 3

Divide by 3

Multiply by 2

Add 4

Multiply by 4

Subtract 5

Divide by 4

Match

Match the equivalent equations

• 7x - 2 = -13

• 7x + 2 = -13

• 2x - 7 = -13

• 7x - 2 = 13

• 2x + 7 = 13

14x - 4 = -26

-21x - 6 = -39

10x - 70 = -65

-28x + 8 = -52

-4x - 14 = -26

• 14x - 4 = -26

• -21x - 6 = -39

• 10x - 70 = -65

• -28x + 8 = -52

• -4x - 14 = -26

Match

Match the equivalent equations

• 4 - 3x = -5

• 4 + 3x = -5

• 3 + 4x = 5

• -3 + 4x = 5

• 5 - 4x = 3

8 - 6x = -10

-8 - 6x = 10

9 + 12x = 15

-6 + 8x = 10

25 - 20x = 15

• 8 - 6x = -10

• -8 - 6x = 10

• 9 + 12x = 15

• -6 + 8x = 10

• 25 - 20x = 15

Multiple Select

Which equations are equivalent to 1 = 11x - 7 ?

• 2 = 22x - 14

• 2 = 22x - 7

• -1 = -11x + 7

• 3 = 11x - 21

• -3 = -33x + 21

Fill in the Blanks

If both sides are multiplied by 9, what is the result?

10 - x = 7

Fill in the Blanks

If both sides are multiplied by -1, what is the result?

x - 1 = -1

Multiple Select

Which equation(s) are equivalent to  $$x-y=-18$$  ?

• $$\frac{x-y}{2}=-9$$  

• $$\frac{x-y}{-9}=-2$$  

• $$\frac{x-y}{-9}=2$$  

• $$-x+y=18$$  

• $$x+y=18$$  

Fill in the Blanks

If both sides are divided by -4, what is the result?

48 = -12x - 4