Certainly! Let's verify the inequality step-by-step for the given values [tex]\( a = 15 \)[/tex], [tex]\( b = -8 \)[/tex], and [tex]\( c = 7 \)[/tex].
1. First, calculate [tex]\( b + c \)[/tex]:
[tex]\[ b + c = -8 + 7 = -1 \][/tex]
2. Next, calculate [tex]\( a \div (b+c) \)[/tex]:
[tex]\[ a \div (b+c) = 15 \div -1 = -15 \][/tex]
3. Then, calculate [tex]\( a \div b \)[/tex]:
[tex]\[ a \div b = 15 \div -8 = -\frac{15}{8} = -1.875 \][/tex]
4. Now, calculate [tex]\( a \div c \)[/tex]:
[tex]\[ a \div c = 15 \div 7 \approx 2.142857142857143 \][/tex]
5. Sum the results of [tex]\( a \div b \)[/tex] and [tex]\( a \div c \)[/tex]:
[tex]\[ (a \div b) + (a \div c) = -1.875 + 2.142857142857143 \approx 0.2678571428571428 \][/tex]
6. Compare [tex]\( a \div (b+c) \)[/tex] with [tex]\( (a \div b) + (a \div c) \)[/tex]:
[tex]\[ -15 \neq 0.2678571428571428 \][/tex]
Thus, we have verified that
[tex]\[ a \div (b+c) \neq (a \div b) + (a \div c) \][/tex]
as [tex]\( -15 \)[/tex] is not equal to approximately [tex]\( 0.2678571428571428 \)[/tex].
