Solving compound inequality
4x-9<9x+6<4x+16
4x-9<9x+6<4x+16
subtract 4x
-9 < 5x + 6 < 16
subtract 6
-15 < 5x < 10
divide by 5
-3 < x < 2
Ah, compound inequalities, a true balancing act! So, let's break it down step by step:
First, we'll solve the left-hand side of the compound inequality:
4x - 9 < 9x + 6
Let's isolate the variable by subtracting 4x from both sides:
-9 < 5x + 6
Next, let's get rid of that pesky 6 by subtracting it from both sides:
-15 < 5x
To finish it off, divide both sides by 5:
-3 < x
Now, let's move on to the right-hand side of the compound inequality:
9x + 6 < 4x + 16
We'll now solve this one similarly. Start by subtracting 4x from both sides:
5x + 6 < 16
Subtract 6 from both sides:
5x < 10
And finally, divide both sides by 5:
x < 2
Now, let's put it all together:
-3 < x < 2
So, the solution to the compound inequality is that x is greater than -3 and less than 2. But hey, don't worry about the math, I promise this clown has got it all under control! 🤡
To solve a compound inequality like 4x - 9 < 9x + 6 < 4x + 16, you need to separate it into two separate inequalities and solve each one individually.
First, let's solve the left side of the compound inequality:
4x - 9 < 9x + 6
1. Start by isolating the variable on one side of the inequality. In this case, let's isolate the x terms on the left side by subtracting 4x from both sides of the inequality:
-9 < 5x + 6
2. Next, isolate the x term by subtracting 6 from both sides:
-9 - 6 < 5x
-15 < 5x
3. Divide both sides of the inequality by 5 to solve for x:
-15/5 < x
-3 < x
So the solution to the left side inequality is x > -3.
Now, let's solve the right side of the compound inequality:
9x + 6 < 4x + 16
1. Isolate the x terms on the left side by subtracting 4x from both sides:
9x - 4x < 16 - 6
5x < 10
2. Divide both sides of the inequality by 5 to solve for x:
5x/5 < 10/5
x < 2
So the solution to the right side inequality is x < 2.
Combining the solutions for both inequalities, we find that the solution to the compound inequality is -3 < x < 2.
4x-9<9x+6<4x+16
subtract 4x
-9 < 5x + 6 < 16
subtract 6
-15 < 5x < 11
divide by 5
-3 < x < 11/5