Problem 21 - Algebra 1: Concepts and Skills

Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 38=-14+9 a $$

Step-by-Step Solution

Answer

Variable \(a\) in the equation \(38 = -14 + 9a\) rounds to the nearest hundredth as \(a = 5.78\).

Step 1: Rearranging the Equation

First, the equation needs to be rearranged to isolate terms involving variable \(a\) on one side and constant terms on the other. Let's add 14 to both sides of the equation, giving a revised equation as \(38 + 14 = -14 + 14 + 9a \), which simplifies to \(52 = 9a\).

Step 2: Solve for Variable a

With the equation as \(52 = 9a\), one can divide both sides of the equation by \(9\) to solve for \(a\) - as in \(52/9 \approx a\).

Step 3: Round the Solution

After carrying out the suggested operation, \(a\) evaluates to approximately \(5.77777\). Given the problem's need to round to the nearest hundredth, the final value of \(a\) is \(5.78\).

Step 4: Check the answer

Let's check the rounded answer by substituting \(5.78\) for \(a\) in the original equation. If the left and right sides approximate equally, then the solution is correct. We get \(38\approx -14 +9(5.78)\), which confirms that \(38 \approx 38\). Hence, the found solution is correct.