−9x+2>18 AND 13x+15≤−4
What do you call a math problem that's feeling a bit negative? A "downright inequality!"
Now, let's solve these inequalities step by step, shall we?
For the first inequality: -9x + 2 > 18
To isolate the variable, let's start by subtracting 2 from both sides:
-9x + 2 - 2 > 18 - 2
Simplifying, we get:
-9x > 16
Now, divide both sides by -9, but remember, when dividing by a negative number, we need to flip the inequality sign:
-9x / -9 < 16 / -9
So, the first inequality simplifies to:
x < -16/9
Now, let's look at the second inequality: 13x + 15 ≤ -4
To isolate the variable, let's subtract 15 from both sides:
13x + 15 - 15 ≤ -4 - 15
Simplifying, we get:
13x ≤ -19
Next, divide both sides by 13:
13x / 13 ≤ -19 / 13
So, the second inequality simplifies to:
x ≤ -19/13
Hope that solves things for you! Just remember, inequalities can be quite strict sometimes, so make sure you give them the space they need to breathe and solve. Keep smiling!
To solve the compound inequality −9x + 2 > 18 && 13x + 15 ≤ −4, we'll solve each inequality separately and find the intersection of their solutions.
1. Solve the first inequality: −9x + 2 > 18
Subtract 2 from both sides:
−9x > 16
Divide both sides by -9 (changing the inequality direction since dividing by a negative number):
x < -16/9
2. Solve the second inequality: 13x + 15 ≤ −4
Subtract 15 from both sides:
13x ≤ -19
Divide both sides by 13:
x ≤ -19/13
3. Find the intersection of the solutions:
We need to find the values of x that satisfy both x < -16/9 and x ≤ -19/13.
Since the second inequality includes equality (≤), the solution set will include the values where x is equal to -19/13. Therefore, we have:
x ≤ -19/13
In conclusion, the solution to the compound inequality −9x + 2 > 18 && 13x + 15 ≤ −4 is x ≤ -19/13.
To solve the inequality −9x+2>18, we need to isolate the variable x and find the range of values that make the inequality true. Let's start by subtracting 2 from both sides of the inequality:
−9x + 2 - 2 > 18 - 2
−9x > 16
Next, we'll divide both sides of the inequality by -9. Here, we need to remember that when dividing by a negative number, the inequality sign must be flipped:
−9x / -9 < 16 / -9
x < -16/9
Therefore, the solution to the inequality −9x+2>18 is x < -16/9.
Now, let's solve the second inequality, 13x + 15 ≤ -4. To isolate the variable x, we'll start by subtracting 15 from both sides:
13x + 15 - 15 ≤ -4 - 15
13x ≤ -19
Next, we divide both sides of the inequality by 13:
13x / 13 ≤ -19 / 13
x ≤ -19/13
Hence, the solution to the inequality 13x + 15 ≤ -4 is x ≤ -19/13.
Therefore, the solution to the system of inequalities −9x+2>18 AND 13x+15≤−4 is x < -16/9 and x ≤ -19/13.
−9x+2>18
x < -16/9
13x+15≤−4
x ≤ -19/13
so, what do you think?