Accepted answer
Answer included
Problem (class6x)
Solve the linear equation and give the value of \(x\):
\[
6\cdot x - 9 = 3\cdot x + 12
\]
A “class6x” style task is interpreted as a fundamental one-variable linear equation where terms in \(x\) are collected on one side and constants on the other.
Solution
Step 1: Move all \(x\)-terms to one side
Subtract \(3\cdot x\) from both sides to keep the equation balanced:
\[
6\cdot x - 3\cdot x - 9 = 12
\]
\[
3\cdot x - 9 = 12
\]
Step 2: Move constants to the other side
Add \(9\) to both sides:
\[
3\cdot x = 12 + 9
\]
\[
3\cdot x = 21
\]
Step 3: Isolate \(x\)
Divide both sides by \(3\):
\[
x = \frac{21}{3} = 7
\]
Step 4: Check by substitution
Substitute \(x=7\) into the original equation:
\[
6\cdot 7 - 9 \;=\; 42 - 9 \;=\; 33
\]
\[
3\cdot 7 + 12 \;=\; 21 + 12 \;=\; 33
\]
Both sides match, so \(x=7\) is correct.
Result: \(x=7\).
The common structure behind many class6x problems is: collect variable terms \((\propto x)\), collect constants, then apply the inverse operation to isolate \(x\).
Visualization (Intersection of Two Lines)
Answer
\(x=7\)
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