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.
- Subtract 7 from both sides:
\[ 4x < -40 - 7 \]
\[ 4x < -47 \]
- Now, divide both sides by 4:
\[ x < \frac{-47}{4} \]
- 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.
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