Problem 15 - Algebra 1: Concepts and Skills

Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 2.2 x=15 $$

Step-by-Step Solution

Answer

The solution to the equation \(2.2x = 15\) to the nearest hundredth, is \(x = 6.82\).

Step 1: Isolate The Variable 'x'

To isolate x, you have to divide both sides of the equation by 2.2. So, the equation turns from \( 2.2x = 15 \) to \( x = 15 ÷ 2.2 \)

Step 2: Solve The Equation

By performing the division operation, you obtain an approximate value for x, which is 6.81818182. We have to, however, round this value to the nearest hundredth.

Step 3: Round The Obtained Value

The rounded value of x, to the nearest hundredth, is 6.82.

Step 4: Check The Rounded Solution

You must substitute the rounded solution for x into the original equation to check the accuracy of the solution. If \(2.2x = 15\) holds true then the solution is correct. Substituting \(x = 6.82\) into the equation gives \(2.2 * 6.82 = 14.904\). This value is not exactly 15 due to the rounding of x, but it's close enough to validate that x=6.82 is a reasonable solution.