Can someone please help with solving compound inequality.
!.) 6x-4<-34 or 3x+10>10
2.) -2<=2x-4<4
I'd appreciate if someone can explain not looking for just answer. Thank you
1. 6x-4< -34, or 3x+10 > 10.
6x-4 < -34.
6x < -34 + 4
6x < -30
X < -5.
3x + 10 > 10.
3x > 10 - 10
3x > 0
X > 0.
2. -2 <= 2x-4 < 4.
Add 4 to each end and the center:
-2 + 4<= 2x-4+4 < 4+4.
2 <= 2x < 8
Divide each end and center by 2:
1 <= X < 4.
The compound inequality is actually 2
inequalities and can be solved separately:
2x-4 => -2, and 2x-4 < 4.
2x-4 => -2.
2x => -2+4
2x=> 2
X => 1.
2x-4 < 4.
2x < 4+4
2x < 8
X < 4.
Solution: 1< = X < 4. or X => 1, and X<4
CHECK:
1. Substitute any number < -5 for X.
Eq2: Subst. any number > 0 for X.
u sure brandon, we needed a line to see
Thank you for showing me how to do these really helps alot.
Sure! I can help you with solving these compound inequalities and explain the process step by step.
1.) 6x - 4 < -34 or 3x + 10 > 10
To solve this compound inequality, we will split it into two separate inequalities and find the solutions for each one. Then, we will combine the solutions to find the final answer.
Starting with the first inequality, 6x - 4 < -34:
1. Add 4 to both sides of the inequality to isolate the variable: 6x - 4 + 4 < -34 + 4
This simplifies to: 6x < -30
2. Divide both sides of the inequality by 6 to solve for x: (6x)/6 < (-30)/6
This simplifies to: x < -5
Now, let's move on to the second inequality, 3x + 10 > 10:
1. Subtract 10 from both sides of the inequality to isolate the variable: 3x + 10 - 10 > 10 - 10
This simplifies to: 3x > 0
2. Divide both sides of the inequality by 3 to solve for x: (3x)/3 > 0/3
This simplifies to: x > 0
Now, we have the individual solutions:
For the first inequality: x < -5
For the second inequality: x > 0
To find the combined solution, we look for values of x that satisfy both inequalities. Looking at the number line, we see that the values that satisfy both x < -5 and x > 0 are x values greater than 0 but less than -5. However, there are no such values since these conditions contradict each other. Therefore, there is no solution for this compound inequality.
2.) -2 <= 2x - 4 < 4
Similar to the previous example, we will split this compound inequality into two separate inequalities to find the solutions for each one.
Starting with the inequality -2 <= 2x - 4:
1. Add 4 to both sides of the inequality to isolate the variable: -2 + 4 <= 2x - 4 + 4
This simplifies to: 2 <= 2x
2. Divide both sides of the inequality by 2 to solve for x: 2/2 <= (2x)/2
This simplifies to: 1 <= x
Now, let's move on to the second inequality, 2x - 4 < 4:
1. Add 4 to both sides of the inequality to isolate the variable: 2x - 4 + 4 < 4 + 4
This simplifies to: 2x < 8
2. Divide both sides of the inequality by 2 to solve for x: (2x)/2 < 8/2
This simplifies to: x < 4
Now, we have the individual solutions:
For the first inequality: x >= 1 (Note that we switch the inequality sign when multiplying or dividing by a negative number)
For the second inequality: x < 4
To find the combined solution, we look for values of x that satisfy both inequalities. Looking at the number line, we find that the values of x greater than or equal to 1 but less than 4 satisfy both inequalities. Therefore, the combined solution for this compound inequality is 1 <= x < 4.
I hope this explanation helps you understand how to solve compound inequalities. If you have any further questions, feel free to ask!