Answer:
Step 1: Transpose everything to one side
12. x²+16x+15-10x+4=0
Step 2: Add the like terms
x² + (16x - 10x) + 15 + 4=0
x² + 6x + 19=0
Step 3: Use the quadratic formula to get the value(s) of x.
a=1 b=6 c=19
therefore, x=... or x
I could be 7- or it could be just 7
1) Graph the corresponding equation \( x = 2 \); this will split the plane into two regions. One of the region represents the solution set.
2) Select a point situated in any of the two regions obtained and test the inequality. If the point selected is a solution, then all the region is the solution set. If the selected point is not a solution, then the other (second) region represents the solution set.
3) Test: In this example, let us for example select the point with coordinates (3 , 2) which is in the region to the right of the line x = 2. If you substitute x in the inequality \( x ≥ 2 \) by 3 it becomes \( 3 ≥ 2 \) which is a true statement and therefore (3 , 2) is a solution. Hence, we can conclude that the region to the right of the vertical line x = 2 is a solution set including the line itself which is shown as a solid line because of the inequality symbol \( ≥ \) contains the \( = \) symbol. The solution set is represented by the blue hash region in the graph below including the line x = 2.
