The inequality in the image is:

$|4x - 2| \leq 10$

This is an absolute value inequality, which can be solved in two cases:

1. $4x - 2 \leq 10$
2. $-(4x - 2) \leq 10$ (or equivalently $4x - 2 \geq -10$)

Let's solve each case:

Case 1: $4x - 2 \leq 10$

Add 2 to both sides: $4x \leq 12$ Now, divide both sides by 4: $x \leq 3$

Case 2: $4x - 2 \geq -10$

Add 2 to both sides: $4x \geq -8$ Now, divide both sides by 4: $x \geq -2$

Combined solution:

The solution to the inequality is: $-2 \leq x \leq 3$

This means the values of $x$ lie between $-2$ and $3$, inclusive.

Would you like further details or explanations?

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Here are some related questions to explore further:

1. How do we graph the solution $-2 \leq x \leq 3$?
2. What changes if the inequality were $|4x - 2| \geq 10$ instead?
3. How do we handle absolute value inequalities when there is a strict inequality $|4x - 2| < 10$?
4. What is the general method for solving absolute value equations or inequalities?
5. Can we express this inequality solution in interval notation?

Tip: When solving absolute value inequalities, always split the problem into two cases (positive and negative).