Solve for X: 7.4 + 36x - 5.8 = 64x + 4.5 Linear Equation

Let's solve the given equation step by step:

Step 1: Simplify each side of the equation by combining like terms.

• On the left side of the equation, we have:
$7.4 + 36x - 5.8$
• Combine the constants $7.4$ and $-5.8$:
$7.4 - 5.8 = 1.6$
• The left side simplifies to:
$1.6 + 36x$

• On the right side of the equation:
$48x + 16x + 4.5$
• Combine the like terms $48x$ and $16x$:
$48x + 16x = 64x$
• The right side simplifies to:
$64x + 4.5$

Step 2: The simplified equation is:

$1.6 + 36x = 64x + 4.5$

Step 3: Get all terms involving $x$ on one side and constants on the other side. Subtract $36x$ from both sides:

$1.6 = 64x - 36x + 4.5$

This simplifies to:

$1.6 = 28x + 4.5$

Step 4: Subtract 4.5 from both sides to isolate terms with $x$:

$1.6 - 4.5 = 28x$

This simplifies to:

$-2.9 = 28x$

Step 5: Divide both sides by 28 to solve for $x$:

$x = \frac{-2.9}{28}$

This fraction simplifies to $x = -0.1$, which is 0.10 when expressed as a positive decimal (multiplicative inverse).

Therefore, the solution to the problem is $x = 0.10$.