-8<2x-4<4 solve the inequality
1 answer:
Answer:
Step-by-step explanation:
The inequality will be split into two
It is know that, if a<b<c
Then a<b and b<c
-8<2x-4<4
Apply that to this
Then,
-8<2x-4. Equation 1
Also,
2x-4<4 equation 2
Solving equation 1
-8<2x-4
Add 4 to both side of the equation
-8+4<2x-4+4
-4<2x
Divide both sides by 2
-4/2<2x/2
-2<x
Note, if a is less than b, then, b is greater than a, e.g. 4 is less than 10, this implies 10 is greater than 4
Therefore,
-2<x
Then, x greater than -2
Equation 2
2x-4<4
Add 4 to both side of the inequalities
2x-4+4<4+4
2x<8
Divide both side by 2
Then,
2x/2<8/2
x<4
Therefore x is between -2 and +4.
Check attachment for graphical solution
You might be interested in
Explanation:
The first step is to figure out what the equation is. When unconventional math symbols are used, and when there are no grouping symbols identifying operands, that can be the most difficult step. Here, we think the equation is supposed to be ...
It usually works well in radical equations to isolate the radical. Here that would mean adding 2 to both sides of the equation, to undo the subtraction of 2.
Now, it is convenient to raise both sides of the equation to the 3rd power.
Finally, we can isolate the variable by undoing the addition of 1. We accomplish that by adding -1 to both sides of the equation.
The equation is solved. The solution is x = 7.