Please help and explain how to solve and graph 4<=2x-8>10
Thanks
8+ 4<=2x-8 + 8 > 10 +8
12<=2x>18
6<=x>9
Thanks :)
To solve the inequality 4 ≤ 2x - 8 > 10, we will break it down into two separate equations and then solve them individually.
First, let's solve the left side of the inequality, 4 ≤ 2x - 8:
Add 8 to both sides of the equation to isolate the variable:
4 + 8 ≤ 2x - 8 + 8
12 ≤ 2x
Divide both sides of the equation by 2 to solve for x:
12/2 ≤ 2x/2
6 ≤ x
Now, let's solve the right side of the inequality, 2x - 8 > 10:
Add 8 to both sides of the equation to isolate the variable:
2x - 8 + 8 > 10 + 8
2x > 18
Divide both sides of the equation by 2 to solve for x:
2x/2 > 18/2
x > 9
So, we have found the solutions for both inequalities: x ≥ 6 and x > 9.
To graph the solution, we can use a number line. Plot a closed circle at 6 (since it is included in the solution) and shade everything to the right of 6. Then, plot an open circle at 9 (since it is not included in the solution) and shade everything to the right of 9.
The final graph will show a shaded region to the right of both 6 and 9 on the number line.