Solve for X: 11.8 + (3/8)x + 6.4 = -(6/24)x - 1.5

To solve the given linear equation, we will follow these steps:

• Simplify fractions in the equation.
• Combine like terms on each side of the equation.
• Move all terms involving $x$ to one side of the equation.
• Move constant terms to the opposite side of the equation.
• Isolate $x$ to find the solution.

Let's begin by simplifying the fractions and combining like terms:

The original equation is:
$11.8 + \frac{3}{8}x + 6.4 = -\frac{6}{24}x - 1.5$

First, simplify $-\frac{6}{24}$ as $-\frac{1}{4}$, because $-\frac{6}{24}$ is equivalent to $-\frac{1}{4}$.

So, the equation becomes:
$11.8 + \frac{3}{8}x + 6.4 = -\frac{1}{4}x - 1.5$

Combine the constant terms on the left side:
$11.8 + 6.4 = 18.2$

The equation now is:
$18.2 + \frac{3}{8}x = -\frac{1}{4}x - 1.5$

To collect all $x$ terms on one side, add $\frac{1}{4}x$ to both sides:
$18.2 + \frac{3}{8}x + \frac{1}{4}x = -1.5$

Convert $\frac{1}{4}$ to $\frac{2}{8}$ so that both fractions have a common denominator:
$\frac{3}{8}x + \frac{2}{8}x = \frac{5}{8}x$

Substituting back, we have:
$18.2 + \frac{5}{8}x = -1.5$

Subtract 18.2 from both sides to isolate the term with $x$:
$\frac{5}{8}x = -1.5 - 18.2$

Calculate the right side:
$-1.5 - 18.2 = -19.7$

So, the equation becomes:
$\frac{5}{8}x = -19.7$

To solve for $x$, multiply both sides by $\frac{8}{5}$ (the reciprocal of $\frac{5}{8}$):
$x = -19.7 \times \frac{8}{5}$

Calculate $-19.7 \times \frac{8}{5}$:
$x = -19.7 \times 1.6 = -31.52$

Thus, the solution to the equation is $x = -31.52$.