Solve for
a
aa.
4
a
+

5

2
+
3.25
a
4a+5=2+3.25a4, a, plus, 5, equals, 2, plus, 3, point, 25, a

a

a=a, equals

The Correct Answer and Explanation is :

To solve for ( a ) in the equation:

[
4a + 5 = 2 + 3.25a
]

we’ll follow these steps:

Step 1: Move all terms involving ( a ) to one side

To isolate ( a ), subtract ( 3.25a ) from both sides:

[
4a – 3.25a + 5 = 2
]

This simplifies to:

[
0.75a + 5 = 2
]

Step 2: Move constant terms to the other side

Next, we want to isolate ( 0.75a ) by moving the constant ( 5 ) to the right side. Subtract ( 5 ) from both sides:

[
0.75a = 2 – 5
]

which simplifies to:

[
0.75a = -3
]

Step 3: Solve for ( a ) by dividing

Now, divide both sides by ( 0.75 ) to isolate ( a ):

[
a = \frac{-3}{0.75}
]

Calculating this gives:

[
a = -4
]

So, the solution is:

[
a = -4
]

---

Explanation of the Solution Process

To solve for ( a ), we used basic algebraic techniques to isolate the variable on one side of the equation. This process involves understanding and applying the properties of equality, which allow us to perform the same operation on both sides of the equation without changing its truth.

In the first step, we moved terms involving ( a ) to the left side and constants to the right, allowing us to combine like terms. Subtracting ( 3.25a ) from both sides resulted in ( 0.75a ), simplifying our equation.

The next step involved isolating ( a ) by moving constants to the other side of the equation. Subtracting ( 5 ) from both sides simplified the constant terms to ( -3 ).

Finally, we solved for ( a ) by dividing by the coefficient ( 0.75 ). This division is a fundamental operation for solving linear equations, as it helps isolate the variable, giving us the answer ( a = -4 ).

Thus, the solution to ( 4a + 5 = 2 + 3.25a ) is ( a = -4 ).