Question
Four times a number, increased by three, is between negative nine and nineteen. Find all the numbers
All the numbers that makes the statement true are given by (Type an inequality or a compound inequality using x as the variable.)
All the numbers that makes the statement true are given by (Type an inequality or a compound inequality using x as the variable.)
Answers
GPT 3.5
Let's call the number x.
According to the given statement, "Four times the number, increased by three, is between negative nine and nineteen."
This can be written as the following inequality:
-9 < 4x + 3 < 19
Now, we can solve this inequality step by step:
-9 < 4x + 3:
Subtracting 3 from all sides: -12 < 4x.
4x + 3 < 19:
Subtracting 3 from all sides: 4x < 16.
Dividing both sides by 4 (since the coefficient of x is 4): x < 4.
Combining the inequalities, we have:
-12 < 4x < 16.
Hence, all the numbers that make the statement true are given by the compound inequality:
-12 < 4x < 16.
According to the given statement, "Four times the number, increased by three, is between negative nine and nineteen."
This can be written as the following inequality:
-9 < 4x + 3 < 19
Now, we can solve this inequality step by step:
-9 < 4x + 3:
Subtracting 3 from all sides: -12 < 4x.
4x + 3 < 19:
Subtracting 3 from all sides: 4x < 16.
Dividing both sides by 4 (since the coefficient of x is 4): x < 4.
Combining the inequalities, we have:
-12 < 4x < 16.
Hence, all the numbers that make the statement true are given by the compound inequality:
-12 < 4x < 16.