How do I solve this:
The absolute value of ax+b is less than or equal to c for the terms of x in terms of a, b, and c where a>0 and c>0
-Then they ask:
The absolute value of ax+b is more than or equal to c for the terms of x in terms of a, b, and c where a>0 and c>0
It's the same thing except the second one is more than...
I have looked at it, and I have no idea what the question is.
ummm... okay l l <--these are going to be absolute value bars.
1.
Solve lax+bl <or equal to c for x in terms of a, b, and c where a>0 and c>0
2.
Now solve lax+bl >or equal to c for x in terms of a, b, and c where a>0 and c>0
this help?
To solve the inequality |ax + b| ≤ c, where a > 0 and c > 0, we can consider two cases:
Case 1: ax + b ≥ 0
In this case, the absolute value of ax + b is equal to ax + b. So the inequality becomes ax + b ≤ c.
To solve this inequality, we can subtract b from both sides:
ax ≤ c - b
Finally, divide both sides by a (since a > 0):
x ≤ (c - b) / a
Case 2: ax + b < 0
In this case, the absolute value of ax + b is equal to -(ax + b). So the inequality becomes -(ax + b) ≤ c.
To solve this inequality, we can multiply both sides by -1 (which reverses the inequality):
ax + b ≥ -c
Now, subtract b from both sides:
ax ≥ -c - b
Lastly, divide both sides by a (since a > 0):
x ≥ (-c - b) / a
To summarize:
- If ax + b ≥ 0, then x ≤ (c - b) / a
- If ax + b < 0, then x ≥ (-c - b) / a
Now, let's consider the second inequality: |ax + b| ≥ c. Since it is the same as the first inequality but with "more than" instead of "less than," we can use the same approach.
Case 1: ax + b ≥ 0
The inequality becomes ax + b ≥ c.
To solve this inequality, we can subtract b from both sides:
ax ≥ c - b
Lastly, divide both sides by a (since a > 0):
x ≥ (c - b) / a
Case 2: ax + b < 0
The inequality becomes -(ax + b) ≥ c.
To solve this inequality, we can multiply both sides by -1 (which reverses the inequality):
ax + b ≤ -c
Now, subtract b from both sides:
ax ≤ -c - b
Finally, divide both sides by a (since a > 0):
x ≤ (-c - b) / a
To summarize:
- If ax + b ≥ 0, then x ≥ (c - b) / a
- If ax + b < 0, then x ≤ (-c - b) / a