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Step-5

Title: Non-linear equations in one variable

Grade: 1300-a Lesson: S1-L6

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve the nonlinear equation: \$ x^2 - 5x + 6 = 0 \$.
2	Step	The given nonlinear equation is	\$x^2 - 5x + 6 = 0\$
3	Hint	Utilizing factorization method	\$ x^2 - 3x - 2x + 6 = 0 \$ \$ x(x - 2) - 3(x - 2) = 0 \$ \$ (x - 2)(x - 3) = 0 \$
4	Step	Find for x values	\$x - 2 = 0 and x - 3 = 0 \$ \$x = 2 and x = 3 \$
5	Step	Therefore, the solutions to the equation \$x^2 - 5x + 6 = 0\$ are \$ x = 2 and x = 3 \$.
6	Choice.A	Correct: This is accurate since it validates both x = 2 and x = 3 as solutions to the given equation	x = 2 and x = 3
7	Choice.B	At x = - 1 and x = 4, the original equation isn’t satisfied, making option B incorrect	x = - 1 and x = 4
8	Choice.C	The equation isn’t satisfied by x = - 2 and x = 5, so they’re not valid solutions for the given equation	x = - 2 and x = 5
9	Choice.D	Option D incorrectly labels one solution as x = - 2 instead of correctly x = 2	x = 3 and x = - 2
10	Answer	Option	A
11	Sumup	Can you briefly tell me what you’ve learned and understood in today’s lesson?

Step

Type

Explanation

Answer

Problem

Solve the nonlinear equation: \$ x^2 - 5x + 6 = 0 \$.

Step

The given nonlinear equation is

\$x^2 - 5x + 6 = 0\$

Hint

Utilizing factorization method

\$ x^2 - 3x - 2x + 6 = 0 \$

\$ x(x - 2) - 3(x - 2) = 0 \$

\$ (x - 2)(x - 3) = 0 \$

Step

Find for x values

\$x - 2 = 0 and x - 3 = 0 \$

\$x = 2 and x = 3 \$

Step

Therefore, the solutions to the equation \$x^2 - 5x + 6 = 0\$ are \$ x = 2 and x = 3 \$.

Choice.A

Correct: This is accurate since it validates both x = 2 and x = 3 as solutions to the given equation

x = 2 and x = 3

Choice.B

At x = - 1 and x = 4, the original equation isn’t satisfied, making option B incorrect

x = - 1 and x = 4

Choice.C

The equation isn’t satisfied by x = - 2 and x = 5, so they’re not valid solutions for the given equation

x = - 2 and x = 5

Choice.D

Option D incorrectly labels one solution as x = - 2 instead of correctly x = 2

x = 3 and x = - 2

Answer

Option

Sumup

Can you briefly tell me what you’ve learned and understood in today’s lesson?