(5.3a−0.8)−(1.6−4.7a)=2a−(a−0.3)
(5.3a−0.8)−(1.6−4.7a)=2a−(a−0.3)
5.3a - 0.8 - 1.6 + 4.7a = 2a - a + 0.3
10a - 2.4 = a + 0.3
Now finish it off.
To solve this equation, we'll start by simplifying both sides of the equation using the distributive property and combining like terms. Let's break it down step by step.
Step 1: Expansion using the distributive property
On the left side of the equation, we have (5.3a - 0.8). Let's distribute this to both terms within the parentheses:
(5.3a - 0.8) - (1.6 - 4.7a) = 2a - (a - 0.3)
Expanding the left side:
5.3a - 0.8 - 1.6 + 4.7a = 2a - (a - 0.3)
Step 2: Combine like terms
On both sides of the equation, we have two terms with 'a', which can be combined. We also have two constant terms that can be combined.
Combining like terms on the left side:
(5.3a + 4.7a) - (0.8 + 1.6) = 2a - (a - 0.3)
Simplifying:
10a - 2.4 = 2a - (a - 0.3)
Step 3: Solve for 'a'
Now, let's isolate the 'a' terms on one side of the equation and the constant terms on the other side.
Moving 2a to the left side by subtracting it:
10a - 2a - 2.4 = - (a - 0.3)
Simplifying:
8a - 2.4 = - a + 0.3
Next, let's isolate the 'a' term on one side:
Adding 'a' to both sides:
8a + a - 2.4 = 0.3
Simplifying:
9a - 2.4 = 0.3
Now, add 2.4 to both sides:
9a = 2.4 + 0.3
Simplifying:
9a = 2.7
Finally, divide both sides by 9 to solve for 'a':
a = 2.7 / 9
a = 0.3
Therefore, the solution to the equation (5.3a - 0.8) - (1.6 - 4.7a) = 2a - (a - 0.3) is a = 0.3.