we know that
The easiest way to find the number that makes the statement true is to substitute the given answers into the equation.
so
Part 1)
\(4.3-2x < x^{2} -2\)
a) For \(x=0\)
\(4.3-2*0 < 0^{2} -2\)
\(12 < -2\) -----> is false
b) For \(x=1\)
\(4.3-2*1 < 1^{2} -2\)
\(10 < -1\) -----> is false
c) For \(x=2\)
\(4.3-2*2 < 2^{2} -2\)
\(8 < 2\) -----> is false
d) For \(x=3\)
\(4.3-2*3 < 3^{2} -2\)
\(6 < 7\) -----> is true
therefore
the answer part 1) is the option D
\(x=3\)
Part 2)
\(6*7-5x+x^{2} \geq x^{3} +x^{2}\)
a) For \(x=5\)
\(6*7-5*5+5^{2} \geq 5^{3} +5^{2}\)
\(42 \geq 150\) ----> is false
b) For \(x=6\)
\(6*7-5*6+6^{2} \geq 6^{3} +6^{2}\)
\(48 \geq 252\) ----> is false
c) For \(x=4\)
\(6*7-5*4+4^{2} \geq 4^{3} +4^{2}\)
\(38 \geq 80\) ----> is false
d) For \(x=3\)
\(6*7-5*3+3^{2} \geq 3^{3} +3^{2}\)
\(36 \geq 36\) ----> is True
therefore
the answer Part 2) is the option D
\(x=3\)
Part 3)
we have
\(8*3-4x\ (\ )\ 7*(10-x)\)
For \(x=3\)
\(8*3-4*3\ (\ )\ 7*(10-3)\)
\(12\ (\ )\ 49\)
we know that
\(12 < 49\)
therefore
the answer Part 3) is the option B
\(<\)
Part 4)
we have
\(9*4-2x\ (\ )\ 5*(11-x)\)
For \(x=8\)
\(9*4-2*8\ (\ )\ 5*(11-8)\)
\(20\ (\ )\ 15\)
we know that
\(20 > 15\)
therefore
the answer Part 4) is the option B
\(>\)
