Answer: c > 12
Step-by-step explanation:tep 1 :
c
Simplify —
3
Equation at the end of step 1 :
c
((2 • —) - 1) - 7 > 0
3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
1 1 • 3
1 = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2c - (3) 2c - 3
———————— = ——————
3 3
Equation at the end of step 2 :
(2c - 3)
———————— - 7 > 0
3
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
7 7 • 3
7 = — = —————
1 3
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
(2c-3) - (7 • 3) 2c - 24
———————————————— = ———————
3 3
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
2c - 24 = 2 • (c - 12)
Equation at the end of step 4 :
2 • (c - 12)
———————————— > 0
3
Step 5 :
5.1 Multiply both sides by 3
5.2 Divide both sides by 2
Solve Basic Inequality :
5.3 Add 12 to both sides
c > 12
Inequality Plot :
5.4 Inequality plot for
0.667 X - 8.000 > 0
One solution was found :
c > 12
, or 
. So the integral from 0 to 2 is
is strictly less than 2, which means we have to treat this as an improper integral.
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