<span>1.
-x = 2 - 3x + 6
-x + 3x = 8
2x = 8
x = 8/2
x = 4
2.
</span><span>Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x </span>← wrong
The correct step: <span>Step 2: 6x − 8 = 12 + 2x
3.
</span>The next step is <span>2m = 8</span>
Answer:
The absolute number of a number a is written as
|a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation
|x|=a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
|x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality
|x|<2
Represents the distance between x and 0 that is less than 2
Whereas the inequality
|x|>2
Represents the distance between x and 0 that is greater than 2
You can write an absolute value inequality as a compound inequality.
−2<x<2
This holds true for all absolute value inequalities.
|ax+b|<c,wherec>0
=−c<ax+b<c
|ax+b|>c,wherec>0
=ax+b<−corax+b>c
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
Step-by-step explanation:
Hope this helps :)
Answer:
(x - 10)² + (y + 9)² = 20
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre to a point on the circle
To calculate r use the distance formula
r = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 9) and (x₂, y₂ ) = (12, - 13)
r = 
= 
= 
, hence
(x - 10)² + (y - (- 9))² = ()², that is
(x - 10)² + (y + 9)² = 20
Answer:
D
Step-by-step explanation:
7^-2 = 1/7^2
The negative means you flip it
1/7^2 times 7^6 is 7^6/7^2 (just multiply).
using rules of exponents, 7^6/7^2 is 7^4 (just subtract 2 from 6)
D is the only one that equals 7^4, as 2 times 2 is 4.
