Algebra Challenge: Solve for X in 72x - 15/8 = 63x - 17/136x + 16

To solve the equation $72x - \frac{15}{8} = 63x - \frac{17}{136}x + 16$, we will proceed step-by-step:

Step 1: Simplify each side of the equation.

• First, look at the right-hand side: $63x - \frac{17}{136}x + 16$. This can be simplified by combining like terms $63x$ and $- \frac{17}{136}x$.

To combine the terms, it's helpful to express them with a common denominator: $63x - \frac{17}{136}x$ can be rewritten as $\left(\frac{63 \times 136}{136}\right)x - \frac{17}{136}x$. Calculate $63 \times 136 = 8568$, so this becomes: \begin{equation} \frac{8568}{136}x - \frac{17}{136}x = \frac{8568 - 17}{136}x = \frac{8551}{136}x. \end{equation}

Step 2: Get all $x$ terms on one side and constants on the other.

• The equation now reads: $72x - \frac{15}{8} = \frac{8551}{136}x + 16$.

• Subtract $\frac{8551}{136}x$ from both sides to move all $x$ terms to the left-hand side.

  $72x - \frac{8551}{136}x = \frac{15}{8} + 16$

Step 3: Simplify the left-hand side involving the $x$ terms.

To simplify $72x - \frac{8551}{136}x$, convert $72$ to a fraction with a common denominator of $136$: $72x = \frac{72 \times 136}{136}x = \frac{9792}{136}x.$

Then: $\frac{9792}{136}x - \frac{8551}{136}x = \frac{1241}{136}x.$

Step 4: Simplify the right-hand side.

$\frac{15}{8} + 16$ can be expressed with a common denominator: $16 = \frac{136}{8}$ Thus, $\frac{15}{8} + \frac{136}{8} = \frac{151}{8}.$

Step 5: Solve for $x$.

The equation is now: $\frac{1241}{136}x = \frac{151}{8}.$ To isolate $x$, multiply both sides by the reciprocal of $\frac{1241}{136}$: $x = \frac{151}{8} \times \frac{136}{1241}.$ \) Performing the multiplication yields: $x = \frac{151 \times 136}{8 \times 1241}.$ Simplifying, this becomes: $x = \frac{20536}{9928}.$ Calculating this fraction, the result simplifies to: $x = \frac{143}{73}.$

Therefore, the solution to the problem is $x = \frac{143}{73}$.