Given the inequalities
(-4 -x)(x+7)(x-3) >0
Step 1: Find the zeros of the polynomials
For (-4 -x)
[tex]\begin{gathered} (-4-x)=0 \\ -4\text{ -x =0} \\ -x=4 \\ x\text{ = -4} \end{gathered}[/tex]
For (x+7)
[tex]\begin{gathered} x\text{ +7 = 0} \\ x\text{ = 0 - 7} \\ x\text{ = -7} \end{gathered}[/tex]
For (x-3)
[tex]\begin{gathered} x-3\text{ =}0 \\ x\text{ = 0+ 3} \\ x\text{ = 3} \end{gathered}[/tex]
Step 2: Draw the range of values on a number line
Step 3: Construct a table to test the range
The table tests the ranges that were obtained from the number line
column 1 shows the range
The values are then tested for each range.
Column 6 shows the product of all the values gotten
The solution to the polynomial is that which was accepted
Since the inequality sign is that of a greater sign, we will accept those that are positive
Hence the solution is
[tex]\begin{gathered} x\text{ < -7 } \\ \text{and} \\ -4
