Solve for X in 36x-52+8x=19x+54-31: Linear Equation Practice

Solve for X:

$36x-52+8x=19x+54-31$

To solve this equation, we'll proceed as follows:

• Step 1: Simplify both sides of the equation by combining like terms.
• Step 2: Move all terms with $x$ to one side of the equation.
• Step 3: Isolate the variable $x$ and solve for it.

Now, let's follow these steps in detail:

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

Left side: $36x - 52 + 8x$ simplifies to $(36x + 8x) - 52 = 44x - 52$.

Right side: $19x + 54 - 31$ simplifies to $19x + (54 - 31) = 19x + 23$.

Thus, the equation becomes:

$44x - 52 = 19x + 23$

Step 2: Move all $x$ terms to one side.

Subtract $19x$ from both sides:

$44x - 19x - 52 = 23$

This simplifies to:

$25x - 52 = 23$

Step 3: Isolate the variable $x$.

Add 52 to both sides:

$25x = 23 + 52$

This gives $25x = 75$.

Finally, divide both sides by 25:

$x = \frac{75}{25}$

Thus, $x = 3$.

Therefore, the solution to the problem is $x = 3$, which corresponds to choice 2.