Answer:
(-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)
Answer:
Express the solution in interval notation.
C. (-5,6)
