Solve this absolute value inequality
8 |u-2| -7<33

In set-builder notation, the set of solutions is:

Step-by-step explanation:

Let's start by isolating the absolute value expression on one side of the inequality:

8 | u - 2 | - 7 < 33

add 7 on both sides:

8 | u - 2 | < 40

divide both sides by 8:

| u - 2 | < 5

Now, in order to remove the absolute value symbols, we need to consider two different cases:

1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:

u - 2 < 5

u < 5 + 2

u < 7

Now the other case;

2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:

2 - u < 5

2 - 5 < u

-3 < u

Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.

In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.

in set builder notation, the set of solutions is given by:

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1