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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Equation with two radicals

Grade: 8-b Lesson: S2-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Discussion: Step1 Step2 Step3 Step4 Step5

Step	Type	Explanation	Answer
1	Problem	Determine the value of q \$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$.
2	Step	The given euqation	\$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$
3	Step	First, simplify the expressions inside the fourth roots	\$root(4) (5 + 5q) = root(4)( -5q - 11)\$
4	Hint	Since the fourth roots of two expressions are equal, the expressions themselves must be equal:	5 + 5q = - 5q - 11
5	Step	Combine like terms by moving all terms involving q to one side and the constants to the other:	5q + 5q = - 11 - 5 10q = - 16
6	Step	Solve for q	\$ q = - \cancel(16) ^ 8 / \cancel(10)^5\$ \$q = - 8/5\$
7	Step	Therefore, the solution to the equation \$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$ is \$ - 8/5\$.
8	Choice.A	Substitute \$q = - 8/5\$ into the original equations; it satisfies them, proving option A as a valid solution	\$q = - 8/5\$
9	Choice.B	Substituting \$- 5/8\$ into the original equations reveals that it does not satisfy them so it is wrong	\$q = - 5/8\$
10	Choice.C	The sign is incorrect: the correct solution should include a negative sign	\$q = 8/5\$
11	Choice.D	Option D suggests \$q = 5/8\$, which does not satisfy the equation, so it is incorrect	\$q = 5/8\$
12	Answer	Option	A
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Determine the value of q \$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$.

Step

The given euqation

\$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$

Step

First, simplify the expressions inside the fourth roots

\$root(4) (5 + 5q) = root(4)( -5q - 11)\$

Hint

Since the fourth roots of two expressions are equal, the expressions themselves must be equal:

5 + 5q = - 5q - 11

Step

Combine like terms by moving all terms involving q to one side and the constants to the other:

5q + 5q = - 11 - 5

10q = - 16

Step

Solve for q

\$ q = - \cancel(16) ^ 8 / \cancel(10)^5\$

\$q = - 8/5\$

Step

Therefore, the solution to the equation \$root(4) (5 - 3q + 8q) = root(4)( -5q - 11)\$ is \$ - 8/5\$.

Choice.A

Substitute \$q = - 8/5\$ into the original equations; it satisfies them, proving option A as a valid solution

\$q = - 8/5\$

Choice.B

Substituting \$- 5/8\$ into the original equations reveals that it does not satisfy them so it is wrong

\$q = - 5/8\$

Choice.C

The sign is incorrect: the correct solution should include a negative sign

\$q = 8/5\$

Choice.D

Option D suggests \$q = 5/8\$, which does not satisfy the equation, so it is incorrect

\$q = 5/8\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?

Discussion: Step1 Step2 Step3 Step4 Step5