Question

solve for w. 0.6(w + 1) = 3(0.7w - 0.3) w =

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation using the distributive property \(a(b + c)=ab+ac\).
For the left - hand side: \(0.6(w + 1)=0.6w+0.6\times1 = 0.6w + 0.6\)
For the right - hand side: \(3(0.7w-0.3)=3\times0.7w-3\times0.3=2.1w - 0.9\)
So the equation becomes \(0.6w + 0.6=2.1w-0.9\)

Step2: Move the terms with w to one side and constants to the other

Subtract \(0.6w\) from both sides of the equation:
\(0.6w+0.6 - 0.6w=2.1w-0.9 - 0.6w\)
Simplify both sides: \(0.6 = 1.5w-0.9\)
Then add \(0.9\) to both sides: \(0.6 + 0.9=1.5w-0.9 + 0.9\)
Simplify: \(1.5 = 1.5w\)

Step3: Solve for w

Divide both sides of the equation \(1.5 = 1.5w\) by \(1.5\):
\(\frac{1.5}{1.5}=\frac{1.5w}{1.5}\)
We get \(w = 1\)

Answer:

\(1\)