Solve: |2x-1|<11 express the solution in interval notation

(-5,6)

Step-by-step explanation:

Study the two possibilities for the expression inside the absolute value symbol: a) the expression 2x-1 is larger or equal zero, in which case its absolute value is the same as 2x-1, and b) the case of 2x-1 smaller than zero for which the absolute value is taken as the opposite (negative of this) value: - 2x+1

Case a) can be then written without using the absolute value symbol as:

2x - 1 < 11 and solving for x (by adding 1 on both sides of the inequality) gives:

2x < 12

Now to find the actual x-values that verify the inequality, we divide both sides by 2:

x < 6

Case b) can be written without using the absolute value symbol as:

- 2x + 1 < 11 so we add 2x to oth sides of the inequality:

1 < 11 + 2x and now subtract 11 from both sides:

-10 < 2x

As we did before, we isolate x on one side by dividing by 2 on both sides of the inequality:

-5 < x

Now we find the interval on the number line that represents all those x values strictly larger than - 5 and smaller than 6.

Such gives us: - 5 < x < 6 which can be written in interval notation as:

(-5, 6)

Case b)