Question

use the inequality 0.05x + 1.13 > -0.24x + 14.18 to complete questions 5 - 7. 5. solve the inequality. 6. write the solution in set - builder notation. 7. graph the solution set.

Explanation:

Step1: Isolate x - terms

Add \(0.24x\) to both sides of the inequality \(0.05x + 1.13> - 0.24x+14.18\).
\(0.05x+0.24x + 1.13> - 0.24x+0.24x + 14.18\), which simplifies to \(0.29x+1.13>14.18\).

Step2: Isolate the variable x

Subtract 1.13 from both sides: \(0.29x+1.13 - 1.13>14.18 - 1.13\), getting \(0.29x>13.05\).
Then divide both sides by 0.29: \(x>\frac{13.05}{0.29}\), so \(x > 45\).

Step3: Write in set - builder notation

The set - builder notation for \(x>45\) is \(\{x|x\in\mathbb{R},x > 45\}\), where \(\mathbb{R}\) represents the set of all real numbers.

Step4: Graph the solution set

On a number line, draw an open circle at 45 (since 45 is not included in the solution set) and draw an arrow to the right to represent all real numbers greater than 45.

Answer:

1. \(x>45\)
2. \(\{x|x\in\mathbb{R},x > 45\}\)
3. On a number - line, an open circle at 45 and an arrow to the right.