The given absolute value equation is:

$|7x| + 4 = 11$

Step 1: Isolate the absolute value term

First, subtract 4 from both sides of the equation:

$|7x| = 11 - 4$ $|7x| = 7$

Step 2: Solve the absolute value equation

The expression $|7x| = 7$ means that $7x$ can be either 7 or -7. So, we have two cases to consider:

1. $7x = 7$
2. $7x = -7$

Step 3: Solve for $x$

Case 1: $7x = 7$

$x = \frac{7}{7} = 1$

Case 2: $7x = -7$

$x = \frac{-7}{7} = -1$

Final Answer:

The solutions to the equation are: $x = 1 \quad \text{or} \quad x = -1$

Would you like more details, or have any further questions?

Related Questions:

1. How do you solve absolute value inequalities?
2. What happens if the absolute value equation has no solution?
3. How would you graph the solution to an absolute value equation?
4. How do you solve multi-step equations involving absolute values?
5. What are some real-life applications of absolute value equations?

Tip:

When solving absolute value equations, always remember that the expression inside the absolute value can result in two possible cases — one positive and one negative.