Question

solve the equation
0.40x + 0.05(10 - x) = 0.10(68)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {} (simplify your answer.)
b. the solution set is {all real numbers}.
c. the solution set is ∅.

Explanation:

Step1: Expand the left side

First, we expand \(0.05(10 - x)\) using the distributive property \(a(b - c)=ab - ac\). So we get:
\(0.40x + 0.05\times10-0.05x = 0.10(68)\)
\(0.40x + 0.5 - 0.05x=6.8\)

Step2: Combine like terms

Combine the \(x\)-terms on the left side. \(0.40x-0.05x = 0.35x\), so the equation becomes:
\(0.35x + 0.5=6.8\)

Step3: Subtract 0.5 from both sides

Subtract \(0.5\) from both sides of the equation to isolate the term with \(x\):
\(0.35x+0.5 - 0.5=6.8 - 0.5\)
\(0.35x = 6.3\)

Step4: Solve for x

Divide both sides by \(0.35\) to solve for \(x\):
\(x=\frac{6.3}{0.35}\)
\(x = 18\)

Answer:

A. The solution set is \(\{18\}\)