Problem 16 - Algebra 1: Concepts and Skills

Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 14-9 x=37 $$

Step-by-Step Solution

Answer

-2.56

Step 1: Apply the Additive Property of Equality

To isolate x, the first step is to apply the additive property of equality, that is, subtract 14 from both sides of the equation: \(-9x = 37 - 14\).

Step 2: Simplify the Equation

The next step is to simplify the right side of the equation by subtracting 14 from 37: \(-9x = 23\).

Step 3: Apply the Division Property of Equality

To get x alone, divide both sides of the equation by -9: \(x = 23 / -9\).

Step 4: Simplify the Equation

Then divide 23 by -9 to find the value of x: \(x = -2.56\) rounded to the nearest hundredth.

Step 5: Check the Solution

To verify the solution, substitute -2.56 back into the original equation and confirm that both sides are equal: \(14 - 9(-2.56) = 14 + 23.04 = 37.04\). This is slightly more than 37 due to the rounding error. The discrepancy is acceptable because the task specified to round the solution to the nearest hundredth.