It appears you've provided an inequality expression: "2|2x-3| < |x+10|." This expression contains absolute values (| |) and a comparison operator (<).

To solve this inequality, we'll need to consider different cases based on the sign of the expressions inside the absolute values.

Case 1: When (2x-3) and (x+10) are both positive.
In this case, the absolute values do not affect the inequality.

2(2x - 3) < x + 10

Simplify and solve for x:

4x - 6 < x + 10

Subtract x from both sides:

3x - 6 < 10

Add 6 to both sides:

3x < 16

Divide by 3:

x < 16/3

Case 2: When (2x-3) and (x+10) are both negative.
In this case, the absolute values become negated.

-2(2x - 3) < -(x + 10)

Simplify and solve for x:

-4x + 6 < -x - 10

Add x to both sides:

-3x + 6 < -10

Subtract 6 from both sides:

-3x < -16

Divide by -3 (remember to reverse the inequality when dividing by a negative number):

x > 16/3

Case 3: When (2x-3) is positive and (x+10) is negative.
In this case, the absolute values do not affect the inequality.

2(2x - 3) < -(x + 10)

Simplify and solve for x:

4x - 6 < -x - 10

Add x to both sides:

5x - 6 < -10

Add 6 to both sides:

5x < -4

Divide by 5:

x < -4/5

Case 4: When (2x-3) is negative and (x+10) is positive.
In this case, the absolute values become negated.

-2(2x - 3) < x + 10

Simplify and solve for x:

-4x + 6 < x + 10

Add 4x to both sides:

6 < 5x + 10

Subtract 10 from both sides:

-4 < 5x

Divide by 5:

-4/5 < x

Now, considering all four cases, the solution set for the inequality "2|2x-3| < |x+10|" is:

x < -4/5 or x > 16/3

So, the values of x that satisfy the inequality are in the range x < -4/5 or x > 16/3.
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