Презентация, доклад по математике на английском языке на тему Absolute value (7 класс)

to:
1. Understand the concept of absolute value of a number.
2. Use the properties of the value of a number to solve equations.

Absolute value

Brad owes $2 and Alec owes $6.
Which one of the following correctly shows this information on the number line?

B

C

D

A

in Chicago was 1° C below zero and the temperature
in Baltimore was 3° C above zero. Which one of the following correctly
shows this information on the number line?

B

C

D

A

the number line?

about it?

все, что знаем по теме.

sign.  
|+3| = 3.   |−3| = 3.
Here is the purely algebraic definition of |x|:
If x ≥ 0, then |x| = x; if x < 0, then |x| = −x.
Geometrically, |x| is the distance of x from 0.

Both 3 and −3 are a distance of 3 units from 0.  |3| = |−3| = 3.  
Distance, in mathematics, is never negative.

Absolute Value-What is it?

zero.

For example "6" is 6 away from zero, but "−6" is also 6 away from zero.
So the absolute value of 6 is 6, and the absolute value of −6 is also 6

absolute value of a real number and the absolute value of its negative are equal.
The absolute value of the product of two real numbers is equal to the product of their absolute values.
The absolute value of the quotient of two real numbers is equal to the quotient of their absolute values.
The absolute value of the sum of two real numbers is less than or equal to the sum of their absolute values.(This property is called triangle inequality)
The absolute values of the differences of two real numbers are equal.

|x| ≥ 0

|x| = |-x|

|x ∙ y|= |x| ∙ |y|

|x / y|= |x| / |y| y ≠ 0

|x + y| ≤ |x| + |y|


|x - y| =| y - x |

Properties of Absolute value

with less than, |a|< b, and the other with greater than, |a|> b.  
They are solved differently.  Here is the first case.

Example 2.  Absolute value less than. |a| < 3.
For that inequaltiy to be true, what values could a have?
Geometrically,  a is less than 3 units from 0.

Therefore, −3 < a < 3. This is the solution.  
The inequality will be true if a has any value between −3 and 3.
In general, if an inequality looks like this --
|a| < b.
-- then the solution will look like this:
−b < a < b for any argument a.

that argument will be 8, or it will be −8.
x − 2 = 8,  or  x − 2 = −8.
We must solve these two equations/уравнения/.  
The first implies/подразумевается/
x = 8 + 2 = 10.
The second implies
x = −8 + 2 = −6.
These are the two solutions:  x = 10 or −6.

argument, 2x − 1, will fall between −5 and 5:
−5 < 2x − 1 < 5.
We must isolate/выделять/ x.  First, add 1 to each term of the inequality:
−5 + 1 <  2x  < 5 + 1
−4 <  2x  < 6.
Now divide each term by 2:
−2 < x < 3.
The inequality will be true for any value of x in that interval.

or zero.
The absolute value of a real number and the absolute value of its negative are equal.
The absolute value of the product of two real numbers is equal to the product of their absolute values.
The absolute value of the quotient of two real numbers is equal to the quotient of their absolute values.
The absolute value of the sum of two real numbers is less than or equal to the sum of their absolute values.(This property is called triangle inequality)
The absolute values of the differences of two real numbers are equal.

|x| ≥ 0

|x| = |-x|

|x ∙ y|= |x| ∙ |y|

|x / y|= |x| / |y| y ≠ 0

|x + y| ≤ |x| + |y|


|x - y| =| y - x |