Question

Solve this problem by writing and solving an inequality. 7 more than four times a number is less than -40

Answer 1

Let's define the variable for the unknown number as \( x \). The phrase "7 more than four times a number" can be mathematically expressed as:

\[
4x + 7
\]

According to the problem, this expression is less than -40. Therefore, we can set up the inequality:

\[
4x + 7 < -40
\]

Now, we will solve the inequality step-by-step.

1. Subtract 7 from both sides:

\[
4x < -40 - 7
\]

\[
4x < -47
\]

2. Now, divide both sides by 4:

\[
x < \frac{-47}{4}
\]

3. Simplify the fraction:

\[
x < -11.75
\]

Therefore, the solution to the inequality is:

\[
x < -11.75
\]

This means that any number less than -11.75 satisfies the original condition.