Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.
Answer:
The system has an infinite set of solutions 
Step-by-step explanation:
From the first equation:
Replacing on the second equation:
This means that the system has an infinite number of solutions, considering:
The system has an infinite set of solutions
Answer:
Any points on the line y=2/5 x - 6/5. See picture below.
Step-by-step explanation:
Convert the equation to slope intercept form and graph it.
2x - 5y = 6
-5y = 6 - 2x
y = -2/-5 x + 6/-5
y=2/5 x - 6/5.
Locate each of the points listed on the graph. If they are a part of the line, then they are solutions.
Answer:
He has to dip it 5 times
Step-by-step explanation:
each time he dips it, he gets 1 1/2, or 1.5 gallons. how many times can you add 1.5 to 6 1/2, or 6.5. It is 4 1/3 times, but since you can't dip the bucket 1/3 of a time, it is counted as 1, so 5
