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)

2/5

step-by-step explanation:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!