−7x−50≤−1 AND−6x+70>−2
−7x−50≤−1 AND−6x+70>−2
-7x ≤ 49 AND -6x > -72
x ≥ -7 AND x < 12
-7 ≤ x < 12
Well, well, well, we've got ourselves a double inequality here! Let's break it down step by step, shall we?
For the first inequality, we have -7x - 50 ≤ -1. To get rid of that pesky -50, we can start by adding 50 to both sides. That gives us -7x ≤ 49. Now, we need to isolate x by dividing both sides by -7. But remember, when you divide an inequality by a negative number, you gotta flip that sign! So, we end up with x ≥ -7.
Now, let's move on to the second inequality, -6x + 70 > -2. To give x a little breathing room, we can start by subtracting 70 from both sides. That gives us -6x > -72. Finally, we can divide both sides by -6. But don't forget to flip that sign! So, we have x < 12.
So, to satisfy both inequalities, we need x to be greater than or equal to -7 and less than 12. In other words, -7 ≤ x < 12. Keep it between the lines, my friend!
To solve the inequality −7x − 50 ≤ −1, you need to isolate the variable x. Here are the steps:
Step 1: Subtract -50 from both sides of the inequality:
−7x − 50 + 50 ≤ −1 + 50
−7x ≤ 49
Step 2: Divide both sides of the inequality by -7. Remember, when dividing by a negative number, you need to flip the inequality sign:
−7x/−7 ≥ 49/−7
x ≥ -7
The solution to the inequality −7x − 50 ≤ −1 is x ≥ -7.
Next, let's solve the inequality −6x + 70 > −2:
Step 1: Subtract 70 from both sides of the inequality:
−6x + 70 - 70 > −2 - 70
−6x > -72
Step 2: Divide both sides of the inequality by -6. Again, remember to flip the inequality sign since we are dividing by a negative number:
−6x/−6 < -72/−6
x < 12
The solution to the inequality −6x + 70 > −2 is x < 12.
To summarize:
For −7x − 50 ≤ −1: x ≥ -7
For −6x + 70 > −2: x < 12
To solve the system of inequalities −7x−50≤−1 AND -6x+70>-2, we will solve each inequality separately and then find the intersection of their solution sets.
Let's start with the first inequality −7x−50≤−1:
Step 1: Add 50 to both sides of the inequality to isolate the term with x.
−7x − 50 + 50 ≤ −1 + 50
−7x ≤ 49
Step 2: Divide both sides of the inequality by -7. Remember that when you divide or multiply both sides by a negative number, you need to flip the inequality sign.
−7x / -7 ≥ 49 / -7
x ≥ -7
So, the solution to the first inequality is x ≥ -7.
Now let's move on to the second inequality -6x + 70 > -2:
Step 1: Subtract 70 from both sides of the inequality to isolate the term with x.
-6x + 70 - 70 > -2 - 70
-6x > -72
Step 2: Divide both sides of the inequality by -6. Again, remember to flip the inequality sign when dividing or multiplying by a negative number.
-6x / -6 < -72 / -6
x < 12
So, the solution to the second inequality is x < 12.
To find the intersection of these two solution sets, we need to find the values of x that satisfy both inequalities. Since one inequality is x ≥ -7 and the other is x < 12, we are looking for the values of x that are greater than or equal to -7 and less than 12.
Therefore, the solution to the system of inequalities is -7 ≤ x < 12.