Solving and Verifying Equations

The video tutorial explains how to solve the equation f(x) = 3√(x+2) by substituting f(x) with 7. The process involves isolating the square root, dividing both sides by 3, and squaring both sides to solve for x. The solution x = 25/9 is verified by substituting it back into the original equation. The tutorial concludes with a confirmation that the solution is correct.

What is the initial equation given in the problem?

• f(x) = 3x^2 + 2

• f(x) = 3/x + 2

• f(x) = 3√x + 2

• f(x) = 3x + 2

Tags

CCSS.HSF.IF.A.2

What value do we substitute for f(x) in the equation?

• 2

• 7

• 3

• 5

Tags

CCSS.HSF.IF.A.2

After substituting 7 for f(x), what is the next step in solving the equation?

• Add 2 to both sides

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 2 from both sides

Tags

CCSS.HSA.REI.A.2

What is the result of dividing both sides by 3 in the equation 5 = 3√x?

• 5 = √x

• 5/3 = √x

• 3/5 = √x

• 15 = √x

Tags

CCSS.HSA.REI.A.2

What operation is performed to eliminate the square root in the equation?

• Taking the cube root

• Dividing by 2

• Squaring both sides

• Multiplying by 2

Tags

CCSS.7.EE.B.4A

What is the value of x after solving the equation?

• 9/25

• 25/9

• 5/3

• 3/5

Tags

CCSS.8.EE.C.7B

How do we verify the solution x = 25/9?

• By solving a new equation

• By checking if x = 25/9 satisfies a different equation

• By substituting x = 25/9 back into the original equation

• By graphing the function

Tags

CCSS.8.EE.A.2

What is the square root of 25/9?

• 5/3

• 9/5

• 3/5

• 25/3

Tags

CCSS.6.EE.B.7

What is the final step in verifying the solution?

• Checking if 5 equals 2

• Checking if 7 equals 5

• Checking if 3 + 2 equals 7

• Checking if 5 + 2 equals 7

Tags

CCSS.8.EE.C.7B

What is the conclusion after verifying the solution?

• The solution is x = 5/3

• The solution is x = 9/25

• The solution is x = 25/9

• The solution is incorrect

Tags

CCSS.8.EE.C.7B