Question

1. three times the difference of federico’s age and 4, increased by 7, is greater than 37. what are possible values of federico’s age? graph his possible ages on the number line.

Explanation:

Step1: Translate the problem into an inequality

Let \( x \) be Federico's age. The problem states "Three times the difference of Federico’s age and 4, increased by 7, is greater than 37". Translating this into an inequality: \( 3(x - 4)+7>37 \)

Step2: Simplify the left - hand side of the inequality

First, expand the expression \( 3(x - 4) \): \( 3x-12 + 7>37 \)
Then, combine like terms: \( 3x-5>37 \)

Step3: Solve for \( x \)

Add 5 to both sides of the inequality: \( 3x-5 + 5>37 + 5 \)
Which simplifies to: \( 3x>42 \)
Divide both sides by 3: \( \frac{3x}{3}>\frac{42}{3} \)
So, \( x > 14 \)

Answer:

Federico's age \( x \) satisfies \( x>14 \). On the number line, we draw an open circle at 14 (since \( x \) is not equal to 14) and shade the region to the right of 14. The possible ages are all real numbers greater than 14.