Solve (3/4)x - 3 = 0.

Step-by-step solution

1. 1

   Note that $\tfrac34x-3$ alone cannot be simplified. The two terms are unlike — $\tfrac34x$ carries a variable and $-3$ does not — so there is nothing to combine. It becomes a solvable problem only once it is set equal to something, here $0$.

2. 2

   Isolate the variable term. Add $3$ to both sides:

   $\frac{3}{4}x=3$

3. 3

   Multiply by the reciprocal instead of dividing by a fraction. The coefficient is $\tfrac34$, whose reciprocal is $\tfrac43$:

   $\frac{4}{3}\cdot\frac{3}{4}x=\frac{4}{3}\cdot3\qquad\Longrightarrow\qquad x=\frac{12}{3}=4$

   Multiplying by $\tfrac43$ is cleaner than dividing by $\tfrac34$, and it makes the cancellation $\tfrac43\cdot\tfrac34=1$ visible.

4. 4

   Alternative: clear the denominator first. Multiplying the whole equation by $4$ at the very start gives $3x-12=0$, hence $3x=12$ and $x=4$ ✓ — the same answer with no fractions at all. Either route is fine; clearing denominators scales better when several fractions appear.

5. 5

   Verify in the original equation. $\tfrac34(4)-3=3-3=0$ ✓, checked in exact rational arithmetic. Geometrically, $y=\tfrac34x-3$ is a line of slope $\tfrac34$ with $y$-intercept $-3$, and $x=4$ is precisely where it crosses the $x$-axis.