To solve the equation:

$|4x - 7| + 4 = 3$

we need to isolate the absolute value term.

Step 1: Subtract 4 from both sides

$|4x - 7| = 3 - 4$ $|4x - 7| = -1$

Step 2: Analyze the Absolute Value Condition

The absolute value of any expression is always non-negative (it’s either zero or positive). Since $-1$ is a negative number, there is no value of $x$ that will satisfy this equation.

Conclusion

The answer is:

• B. There is no solution.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What are the general steps to solve absolute value equations?
2. Can an absolute value equation have two solutions?
3. How would the solution change if the right side of the equation were positive?
4. What does it mean for an absolute value equation to have no solution?
5. How can we graph absolute value equations to visualize their solutions?

Tip: When solving absolute value equations, always check if the right side is negative. If it is, there is no solution.