I'll show you how to do one of the equations and one of the inequalities. All the others are done exactly in the same way: you'll only have to change the numbers, and it will be a good exercise.

Equations

Let's take the first equality as an example: we have

$|x-2|=5$

By definition, the absolute value of a number is the positive version of that number: if the number is already positive the absolute value doesn't change it; if a number is negative the absolute value changes its sign.

So, if the absolute value of a number is 5, than that number was already 5, or it was -5, and the absolute value changed it to positive 5.

So, the solutions are given by

$|x-2|=5 \iff x-2=5 \lor x-2 = -5 \iff x=7 \lor x=-3$

Inequalities

Again, we'll use the first one as example. We have

$|x+4|\geq 7$

By the same logic as before, the absolute value of a number is greater than 7 if the number is already greater than 7, or if it is smaller than -7. For example, we have |-10|=10>7.

So, we have

$|x+4|\geq 7 \iff x+4 \geq 7 \lor x+4 \leq -7 \iff x \geq 3 \lor x \leq -11$

Instead, if we have an inequality with the "less than" sign, we have for example

$|x-5|\leq 8 \iff -8 \leq x-5 \leq 8 \iff -3 \leq x \leq 13$

4 0

3 years ago

SOMEONE HELP ME WITH THIS QUESTION PLEASE!!!!

dusya [7]

Answer:

E(-2, -1.5)

Step-by-step explanation:

<u>Coordinates of the points C and D:</u>

C(1, 6), D(-3, -4)

The point E has coordinates of (x, y).

The point E is at 3/4 of CD from C and 1/4 of CD from the point D.

<u>Find coordinates of E:</u>

x = -3 + 1/4(1 + 3) = -3 + 1 = -2
y = -4 + 1/4(6 + 4) = -4 + 2.5 = -1.5

4 0

2 years ago

How much degrees turn is from 1 o'clock to 2oclock

defon

Answer:

how much degrees turn is from 1 o'clock to 2oclock

31 Degrees

4 0

2 years ago