Question

solve the equation.
0.9(x + 60) + 0.7x = 118

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: Distribute 0.9

First, we distribute the 0.9 across the terms in the parentheses: \(0.9(x + 60) = 0.9x + 0.9 \times 60 = 0.9x + 54\). So the equation becomes \(0.9x + 54 + 0.7x = 118\).

Step2: Combine like terms

Next, we combine the \(x\)-terms: \(0.9x + 0.7x = 1.6x\). So now the equation is \(1.6x + 54 = 118\).

Step3: Subtract 54 from both sides

We subtract 54 from both sides to isolate the term with \(x\): \(1.6x + 54 - 54 = 118 - 54\), which simplifies to \(1.6x = 64\).

Step4: Divide by 1.6

Finally, we divide both sides by 1.6 to solve for \(x\): \(x = \frac{64}{1.6} = 40\).

Answer:

A. The solution set is \(\{40\}\)