Is The Inequality Statement True Or False?

Practice using substitution to determine whether or not an inequality statement is true or false.

Which inequality is true when the value of a is −15?

1. \( -a + 10 \leq 3 \)
2. \( -a + 10 \leq -3 \)
3. \( a + 10 \leq -3 \)
4. \( a + 10 \geq -3 \)

Let's evaluate each inequality when the value of \(a\) is -15 and determine which one is true.

1. \( -a + 10 \leq 3 \)
2. \( -a + 10 \leq -3 \)
3. \( a + 10 \leq -3 \)
4. \( a + 10 \geq -3 \)

Let's substitute \(a = -15\) into each inequality:

1. \( -(-15) + 10 \leq 3 \)
   \( 15 + 10 \leq 3 \)
   \( 25 \leq 3 \) (which is false)

2. \( -(-15) + 10 \leq -3 \)
   \( 15 + 10 \leq -3 \)
   \( 25 \leq -3 \) (which is false)

3. \( -15 + 10 \leq -3 \)
   \( -5 \leq -3 \) (which is true)

4. \( -15 + 10 \geq -3 \)
   \( -5 \geq -3 \) (which is false)

So, the 3rd choice is true and the other 3 choices are false.

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