Solve for X: 17.5 - 18x - 5.5x = 19.2 + 14½ - 5x Linear Equation

To solve the equation $17.5 - 18x - 5.5x = 19.2 + 14\frac{1}{2} - 5x$, follow these steps:

Step 1: Combine like terms on both sides of the equation.

• On the left side, combine $-18x - 5.5x$, which simplifies to $-23.5x$.
• On the right side, simplify $19.2 + 14.5 - 5x$. The fraction $14\frac{1}{2}$ is converted to decimal form as $14.5$, giving $19.2 + 14.5 = 33.7$.

Step 2: Rewrite the equation with the simplified terms:

$17.5 - 23.5x = 33.7 - 5x$.

Step 3: Get all terms involving $x$ on one side of the equation and constant terms on the other.

• Add $5x$ to both sides to move all $x$ related terms to the left:
• $17.5 - 23.5x + 5x = 33.7$

This further simplifies to $17.5 - 18.5x = 33.7$.

Step 4: Isolate the term with $x$ by subtracting $17.5$ from both sides:

$-18.5x = 33.7 - 17.5$.

The right side evaluates to $16.2$.

Thus, we have $-18.5x = 16.2$.

Step 5: Solve for $x$ by dividing both sides by $-18.5$:

$x = \frac{16.2}{-18.5} \approx -0.8757$.

Rounding $-0.8757$ to two decimal places gives $x = -0.87$.

Therefore, the solution to the equation is $x = -0.87$.

This corresponds to option 2 in the given choices.