Question

Inequalities Unit Test
10 of 1510 of 15 Items









Question
Fifteen less than four times a number is more than 49. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x
as your variable and write your x
term first.

Answer 1

To represent the statement "Fifteen less than four times a number is more than 49" using an inequality, we can break down the statement as follows:

1. **Four times a number**: This can be represented as \(4x\), where \(x\) is the number.
2. **Fifteen less than four times a number**: This translates to \(4x - 15\).
3. **Is more than 49**: This indicates that we will use the greater than symbol (>) to indicate that what we have is greater than 49.

Putting this together, we get the inequality:

\[
4x - 15 > 49
\]

Now, we will solve the inequality for \(x\):

1. Add 15 to both sides:
\[
4x - 15 + 15 > 49 + 15
\]
\[
4x > 64
\]

2. Divide both sides by 4:
\[
x > 16
\]

Thus, the possible values of \(x\) are those that are greater than 16. The solution can be expressed in interval notation as:

\[
(16, \infty)
\]

So, the final answer includes the inequality:

\[
4x - 15 > 49
\]

And the solution is \(x > 16\).