Question

If ( 3x - 7 = 20 ), then the value of (x) is:

• A. 7
• B. 8
• C. 9
• D. 10

Hint:

For quick multiple-choice algebraic problems, simply substitute the given choices directly into the expression to find the one that fits!
• Try option (b) $x = 8$: $3(8) - 7 = 24 - 7 = 17 \neq 20$
• Try option (c) $x = 9$: $3(9) - 7 = 27 - 7 = 20 = 20$ Option (c) balances the equation instantly without any scratch work!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem presents a standard linear equation in one variable. To isolate and solve for the unknown variable $x$, we apply inverse mathematical operations systematically to both sides of the expression. Any operation executed on the left side must be identically duplicated on the right side to keep the algebraic balance perfectly maintained.

Step 2: Key Formula or Approach:
For any linear mathematical structure matching $ax - b = c$: 1. Add $b$ to both sides to segregate the variable multiplier term: $ax = c + b$
2. Divide both sides by the coefficient $a$ to completely isolate the variable: $x = \frac{c + b}{a}$

Step 3: Detailed Explanation:
Let's begin with the provided algebraic statement: $$3x - 7 = 20$$ First, cancel out the subtraction of $7$ by performing the inverse operation—adding $7$ to both sides of the equality: $$3x = 20 + 7$$ $$3x = 27$$ Next, eliminate the coefficient multiplier $3$ by dividing both sides of the equation by $3$: $$x = \frac{27}{3}$$ $$x = 9$$ We can confidently verify this answer by plugging $x = 9$ back into our initial expression: $$\text{LHS} = 3(9) - 7 = 27 - 7 = 20 = \text{RHS}$$ Since both sides match perfectly, our solution is confirmed to be accurate.

Step 4: Final Answer:
The value of $x$ is 9.