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### Case-Based Questions

Case I: One day, the principal of Deen School, Mr. Sukhdev, visited all the classes. During his visit to class VII, he found the teacher teaching his favorite concept, "Simple Equations." Remembering his school days, he shared some memories of learning the chapter "Simple Equations" and asked a few questions related to this topic to test the students' understanding.

1. The equation of the statement "4 less than thrice a number [tex]\( m \)[/tex] is 14" is:
- (a) [tex]\( 4 - 3m = 14 \)[/tex]
- (b) [tex]\( 3m - 4 = 14 \)[/tex]
- (c) [tex]\( 5m - 14 = 4 \)[/tex]
- (d) [tex]\( 5m + 4 = 14 \)[/tex]

2. The solution of the equation [tex]\( 20 - (2x - 5) = 25 \)[/tex] is:
- (a) [tex]\( x = 5 \)[/tex]
- (b) [tex]\( x = 0 \)[/tex]
- (c) [tex]\( x = -5 \)[/tex]
- (d) [tex]\( x = 25 \)[/tex]

3. The value of the variable which makes the equation a true statement is called the _____ of the equation.



Answer :

GinnyAnswer
Sure! Let's solve each part of the question step-by-step.

### Part 1: Formulating the Equation
The problem statement is: "4 less than thrice of a number [tex]\( m \)[/tex] is [tex]\( 14 \)[/tex]".

Let's break it down:
- "Thrice of a number [tex]\( m \)[/tex]" means [tex]\( 3m \)[/tex].
- "4 less than thrice of a number" means we need to subtract 4 from [tex]\( 3m \)[/tex], which results in [tex]\( 3m - 4 \)[/tex].
- This is said to be equal to 14.

Putting it all together, we get the equation:
[tex]\[ 3m - 4 = 14 \][/tex]

So, the correct option is:
(b) [tex]\( 3m - 4 = 14 \)[/tex]

### Part 2: Solving the Equation
We need to solve the equation [tex]\( 20 - (2x - 5) = 25 \)[/tex].

Step-by-step simplification:
1. Distribute the minus sign inside the parenthesis:
[tex]\[ 20 - 2x + 5 = 25 \][/tex]

2. Combine the like terms:
[tex]\[ 25 - 2x = 25 \][/tex]

3. Subtract 25 from both sides to isolate the [tex]\( -2x \)[/tex] term:
[tex]\[ -2x = 0 \][/tex]

4. Divide both sides by [tex]\( -2 \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 0 \][/tex]

So, the correct option is:
(b) [tex]\( x = 0 \)[/tex]

### Part 3: Definition
The question asks for the value of the variable which makes the equation a true statement. This is known as the solution of the equation.

So, the correct answer is:
The value of the variable which makes the equation a true statement is called the solution of the equation.

### Summary
1. The equation of the statement "4 less than thrice of a number [tex]\( m \)[/tex] is 14" is: (b) [tex]\( 3m - 4 = 14 \)[/tex].
2. The solution of the equation [tex]\( 20 - (2x - 5) = 25 \)[/tex] is: (b) [tex]\( x = 0 \)[/tex].
3. The value of the variable which makes the equation a true statement is called the solution of the equation.

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