−15x+4≤109 OR −6x+70>−2
−15x+4 ≤ 109 OR −6x+70 > −2
-15x ≤ 105 OR -6x > - 72
x ≥ 7 OR x < 12
That would cover the entire number line, so x ∈ R
Oh, I see you're trying to solve an inequality! Let me help you in my own silly way:
For the first one, −15x + 4 ≤ 109, we can start by subtracting 4 from both sides:
−15x ≤ 109 - 4
−15x ≤ 105
Now, to get x by itself, we divide both sides by -15. But be careful! When we divide by a negative number, the inequality flips:
x ≥ 105 ÷ -15
x ≥ -7
So, the solution for the first inequality is x ≥ -7. But remember, don't invite -7 to any parties, because it's a negative number!
Now, on to the second one, −6x + 70 > -2. Let's start by subtracting 70 from both sides:
−6x > -2 - 70
−6x > -72
To solve for x, we divide both sides by -6. But again, remember that dividing by a negative number flips the inequality sign:
x < -72 ÷ -6
x < 12
So, the solution for the second inequality is x < 12. In other words, you better stay on the left side of 12, because that's where the party is at!
Hope that puts a smile on your face while solving these inequalities!
To solve the inequality −15x + 4 ≤ 109, we follow these steps:
Step 1: Subtract 4 from both sides:
−15x ≤ 109 - 4
−15x ≤ 105
Step 2: Divide both sides by −15. Since we are dividing by a negative number, the inequality sign flips:
x ≥ 105/(-15)
Step 3: Simplify the division:
x ≥ -7
Now, let's solve the inequality −6x + 70 > −2:
Step 1: Subtract 70 from both sides:
−6x > −2 - 70
−6x > -72
Step 2: Divide both sides by −6. But be aware that when dividing by a negative number, the inequality sign flips:
x < -72/(-6)
Step 3: Simplify the division:
x < 12
So, the solutions to the inequalities are:
-7 ≤ x < 12
To solve the inequality −15x + 4 ≤ 109, we need to isolate the variable x.
Step 1: Subtract 4 from both sides of the inequality:
−15x + 4 - 4 ≤ 109 - 4
−15x ≤ 105
Step 2: Divide both sides of the inequality by -15. Remember, when you divide by a negative number, you need to reverse the inequality sign:
−15x / -15 ≥ 105 / -15
x ≥ -7
So the solution to the inequality −15x + 4 ≤ 109 is x ≥ -7.
Now 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. Remember, when you divide by a negative number, you need to reverse the inequality sign:
−6x / -6 < -72 / -6
x < 12
So the solution to the inequality −6x + 70 > −2 is x < 12.
Putting the two solutions together, we have:
x ≥ -7 OR x < 12.