Question

is my working step wrong? the quaestion is find the range of values of x that satisfy the inequalities by using basic definition​

Answer 1

x < -2

Explanation:

2|x| > 3x + 10

Divide both sides by 2.

|x| > 1.5x + 5

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An absolute value inequality of the form

|X1| > X2

where X1 and X2 are expressions in x is solved by solving the compound inequality

X1 > X2 or X1 < -X2

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Back to your problem.

|x| > 1.5x + 5

x > 1.5x + 5 or x < -(1.5x + 5)

-0.5x > 5 or x < -1.5x - 5

x < -10 or 2.5x < -5

x < -10 or x < -2

Since x < -10 is included in x < -2, the solution is

x < -2