-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
Answer:
c. 24 is a solution
Step-by-step explanation:
Given equation:
To test the numbers 22, 23, 24, 25 for the solution.
Solution:
In order to test the given number for the solution, we will plugin each number in the unknown variable and see if it satisfies the equation.
1)
Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.
The above statement can never be true and hence 22 is not a solution.
2)
The fractions can no further be reduced.
The statement can never be true and hence 23 is not a solution.
3)
Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.
The above statement is always true and hence 24 is a solution.
4)
The fractions can no further be reduced.
The statement can never be true and hence 25 is not a solution.