Question

problem 7: spiral review select all of the true statements. □ 2.25 > 2 □ 2.25 < 2 □ -2.25 > -2 □ -2.25 < -2 □ 2.25 > -2

Explanation:

Step1: Analyze \(2.25 > 2\)

Compare the two positive numbers. \(2.25\) is \(2 + 0.25\), so \(2.25\) is greater than \(2\). So \(2.25>2\) is true.

Step2: Analyze \(2.25 < 2\)

Since \(2.25>2\) (from Step 1), \(2.25 < 2\) is false.

Step3: Analyze \(-2.25 > -2\)

For negative numbers, the one with the larger absolute value is smaller. \(|-2.25| = 2.25\) and \(|-2| = 2\). Since \(2.25>2\), \(-2.25 < -2\), so \(-2.25 > -2\) is false.

Step4: Analyze \(-2.25 < -2\)

As in Step 3, \(|-2.25| = 2.25\) and \(|-2| = 2\). Since \(2.25>2\), \(-2.25\) is less than \(-2\). So \(-2.25 < -2\) is true.

Step5: Analyze \(2.25 > -2\)

Positive numbers are greater than negative numbers. So \(2.25\) (positive) is greater than \(-2\) (negative). So \(2.25 > -2\) is true.

Answer:

• \(2.25 > 2\) (True)
• \(-2.25 < -2\) (True)
• \(2.25 > -2\) (True)

So the true statements are:
\(\boldsymbol{2.25 > 2}\), \(\boldsymbol{-2.25 < -2}\), \(\boldsymbol{2.25 > -2}\)