Question

1. joshua plans to save more than $750 for his upcoming vacation. if x represents the amount of money joshua saves for his upcoming vacation, write an inequality that represents the amount of money joshua saves.
2. represent possible amounts that joshua plans to save on the number line.
3. the inequality 7.5 > x is represented on a number line with an ____ circle at 7.5 and shaded to the ____.
4. write an inequality to represent 7 3/4 less than g.
5. write two correct ways to read, 9.05 > x.

Explanation:

Step1: Translate the statement into an inequality

Since Joshua plans to save more than $750$, and $x$ represents the amount he saves, the inequality is \(x>750\).

Step2: Represent \(x > 750\) on the number line

On the given number line, we draw an open circle at \(750\) (because \(x\) is not equal to \(750\)) and shade to the right (since \(x\) is greater than \(750\)).

Step3: Analyze the inequality \(7.5>x\)

The inequality \(7.5 > x\) (or \(x<7.5\)) is represented on a number line with an open circle at \(7.5\) (because the value \(7.5\) is not included in the solution set) and shaded to the left (since \(x\) is less than \(7.5\)).

Step4: Translate the statement into an inequality

The phrase “\(7\frac{3}{4}\) less than \(g\)” means \(7\frac{3}{4}

Step5: Read the inequality \(9.05>x\)

Two correct ways to read \(9.05 > x\) are: “\(9.05\) is greater than \(x\)” and “\(x\) is less than \(9.05\)”.

Answer:

1. \(x > 750\)
2. Open circle at \(750\) and shaded to the right on the number - line.
3. Open, left
4. \(7.75
5. “\(9.05\) is greater than \(x\)”; “\(x\) is less than \(9.05\)”