Question

1 solve the equation. 0.3(1.4 - 0.2x) = 0.06(0.6x - 1)

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side: \(0.3\times1.4-0.3\times0.2x = 0.42-0.06x\).
Expand the right - hand side: \(0.06\times0.6x-0.06\times1=0.036x - 0.06\).
So the equation becomes \(0.42-0.06x=0.036x - 0.06\).

Step2: Move the terms with x to one side

Add \(0.06x\) to both sides of the equation:
\(0.42-0.06x + 0.06x=0.036x-0.06 + 0.06x\)
Simplify to get \(0.42=0.096x-0.06\).

Step3: Isolate the term with x

Add \(0.06\) to both sides:
\(0.42 + 0.06=0.096x-0.06 + 0.06\)
Simplify: \(0.48 = 0.096x\).

Step4: Solve for x

Divide both sides by \(0.096\):
\(x=\frac{0.48}{0.096}\)
Calculate \(\frac{0.48}{0.096}=5\).

Answer:

\(x = 5\)