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

Answer 1

To solve the problem, we first need to translate the wording into a mathematical inequality.

Let \( x \) represent the unknown number. The phrase "four times a number" can be written as \( 4x \). When we add 7 to this, we have:

\[ 4x + 7 \]

The problem states this expression is "less than -40," which we write as:

\[ 4x + 7 < -40 \]

Now, we can solve the inequality step by step.

1. Subtract 7 from both sides:

\[ 4x < -40 - 7 \] \[ 4x < -47 \]

2. Next, divide both sides by 4:

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

3. Simplifying the fraction gives:

\[ x < -11.75 \]

Thus, the solution to the inequality is:

\[ x < -11.75 \]

This means any number less than \(-11.75\) satisfies the condition described in the problem.