Will you please check this and make sure that I am right?
26. 5>-3x+4 or 9< equal to -3x+2
this would be (-infinate,-7/3] & (-1/3,infinante)
You're almost there:
5>-3x+4 or 9< equal to -3x+2
this would be
(-∞,-7/3] ∪ (-1/3,∞)
Thank you for your help. I think that I understand better now.
You're welcome.
Post again if you have other questions.
To check if your answer is correct, we need to solve the given inequalities individually and then combine their solutions.
Let's start with the first inequality: 5 > -3x + 4.
To isolate x, we can subtract 4 from both sides of the inequality:
5 - 4 > -3x + 4 - 4
1 > -3x
Next, we divide both sides by -3, remembering to flip the inequality sign since we are dividing by a negative number:
1/-3 < -3x/-3
-1/3 < x
So the solution to the first inequality is x > -1/3.
Moving on to the second inequality: 9 <= -3x + 2.
To isolate x, we can subtract 2 from both sides of the inequality:
9 - 2 <= -3x + 2 - 2
7 <= -3x
Next, we divide both sides by -3, again remembering to flip the inequality sign:
7 / -3 >= -3x / -3
-7/3 >= x
So the solution to the second inequality is x <= -7/3.
Now, to find the combined solution, we need to consider both inequalities together. Based on the original question, we have:
x > -1/3 or x <= -7/3
Therefore, the correct solution is (-∞, -7/3] U (-1/3, ∞).