Solve the Fraction Equation: Discover X in (x - 4)/18 = 7/9

To solve the equation $\frac{x-4}{18} = \frac{7}{9}$, we'll follow these steps:

• Step 1: Apply the principle of cross-multiplication to eliminate fractions.

• Step 2: Solve for the linear expression in terms of $x$.

• Step 3: Isolate $x$ and solve the equation completely.

Now, let's work through each step:
Step 1: Cross-multiply to eliminate the fractions. The equation becomes:

$(x-4) \cdot 9 = 18 \cdot 7 \\ 9(x-4) = 126$

Step 2: Distribute the 9 on the left-hand side:

$9x - 36 = 126$

Step 3: Add 36 to both sides to isolate the term with $x$:

$9x = 126 + 36 9x = 162$

Step 4: Divide both sides by 9 to solve for $x$:

$x = \frac{162}{9} \\ x = 18$

Therefore, the solution to the equation is $x = 18$.