Let's solve the inequality:

Step 1: Write the inequality

$7 + 4x < -21$

Step 2: Isolate the term with $x$

Subtract 7 from both sides: $4x < -21 - 7$ $4x < -28$

Step 3: Solve for $x$

Now, divide both sides by 4: $x < -7$

Solution

The solution to the inequality is: $x < -7$

Graphing the Solution on a Number Line

To graph this on the number line:

1. Locate -7 on the number line.
2. Place an open circle at -7 (since $x$ is strictly less than -7 and does not include -7 itself).
3. Shade all points to the left of -7, as $x$ represents values less than -7.

Let me know if you want further details or have questions.

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Related Questions

1. How do we solve inequalities with a variable on both sides?
2. What does it mean to have a "strict" inequality?
3. How would we graph $x \leq -7$ instead of $x < -7$?
4. How do inequalities change when multiplying by a negative number?
5. What are some real-life examples of inequalities?

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Tip

When dividing or multiplying both sides of an inequality by a negative number, remember to reverse the inequality symbol!