Answer:
a = 0.3
General Formulas and Concepts:
Pre-Algebra
- Order of Operations: BPEMDAS
- Equality Properties
Explanation:
Step 1: Define equation
(5.3a - 0.8) - (1.6 - 4.7a) = 2a - (a - 0.3)
Step 2: Solve for a
- Distribute negative: 5.3a - 0.8 - 1.6 + 4.7a = 2a - a + 0.3
- Combine like terms: 10a - 2.4 = a + 0.3
- Subtract a on both sides: 9a - 2.4 = 0.3
- Add 2.4 on both sides: 9a = 2.7
- Divide 9 on both sides: a = 0.3
Step 3: Check
Plug in a to verify it's a solution.
- Substitute: (5.3(0.3) - 0.8) - (1.6 - 4.7(0.3)) = 2(0.3) - (0.3 - 0.3)
- Multiply: (1.59 - 0.8) - (1.6 - 1.41) = 0.6 - 0
- Subtract: 0.79 - 0.19 = 0.6
- Subtract: 0.6 = 0.6
Here we see that 0.6 does indeed equal 0.6.
∴ a = 0.3 is a solution of the equation.