Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
1 answer:
Answer: x≤ -0.5
Step-by-step explanation: Graph the two lines or solve for x:
2x – 6 ≥ 6(x – 2) + 8
2x – 6 ≥ 6x – 12 + 8
2x – 6 ≥ 6x – 4
-4x ≥ 2
x ≤ -1/2 [Inequality is reversed when multiplying or dividing by a negative number]
The number line is anything less than or equal to - 1/2
Or one can plot each side of the inequality and note the interception point (x = -(1/2)).
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max = 5, min = -1
mid = (5-1)/2 = 2
{observe for sinx,
max = 1, min, = -1, mid=0}
since mid=2 we can let the function
y=a•sin(bx+c)+2
2a=max-min=6
a=3
y=3sin(bx+c)+2
the graph cross (0,2) so
2=3sin(c)+2
3sin(c)=0
c=0 or c=π
since the graph go down after (0,2), then we choose c=π.
max=5 with x=-1, so
5=3sin(-b+π)+2
sin(-b+π)=1
b=π/2
at last the get the exact equation, that's