Isolating Variables and Solving Equations

The video tutorial explains how to solve the equation -4 + 7.4d = 55.8 using two methods. The first method involves solving the equation with decimals by isolating the variable D. The second method eliminates decimals by multiplying both sides by 10 before solving. Both methods yield the same solution, D = -7. The tutorial concludes with a verification step, substituting the solution back into the original equation to confirm its correctness.

What is the main objective when solving the equation -4 + 7.4d = 55.8?

• To find the value of D that makes the equation true

• To eliminate all variables from the equation

• To find the value of D that makes the equation false

• To convert the equation into a quadratic form

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CCSS.HSA.REI.A.1

In the first method, what is the initial step to isolate D?

• Multiply both sides by 7.4

• Add 4 to both sides

• Subtract 7.4 from both sides

• Divide both sides by 4

Tags

CCSS.HSA.REI.A.1

Why can't we subtract 7.4 from both sides to isolate D?

• Because 7.4 is divided by D

• Because 7.4 is multiplied by D

• Because 7.4 is added to D

• Because 7.4 is subtracted from D

Tags

CCSS.HSA.REI.A.1

What operation is used to solve 7.4 * D = 51.8?

• Addition

• Subtraction

• Multiplication

• Division

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CCSS.5.NBT.B.7

What is the result of dividing 51.8 by 7.4?

• 6

• 7

• 8

• 9

Tags

CCSS.7.EE.B.4A

In the second method, what is the first step to eliminate decimals?

• Divide both sides by 10

• Add 10 to both sides

• Multiply both sides by 10

• Subtract 10 from both sides

Tags

CCSS.7.EE.B.4A

What is the equivalent equation after eliminating decimals in the second method?

• -40 + 74d = 558

• -4 + 7.4d = 55.8

• 4 + 7.4d = 55.8

• 40 + 74d = 558

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CCSS.8.EE.C.7B

What is the final value of D using both methods?

• -7

• -6

• 6

• 8

Tags

CCSS.7.EE.B.4A

How do we verify the solution of the equation?

• By checking if -4 + 7.4 * D equals 0

• By checking if -4 + 7.4 * D equals 100

• By checking if -4 + 7.4 * D equals 55.8

• By checking if -4 + 7.4 * D equals -55.8

Tags

CCSS.8.EE.C.7B

What is the significance of verifying the solution?

• To ensure the solution is incorrect

• To confirm the solution satisfies the original equation

• To find an alternative solution

• To simplify the equation further

Tags

CCSS.8.EE.C.7B