SOLUTION: I need help with this equation Solve the compound inequality. Then graph the solution 8x 11 < 5 or 4x - 7 > 13

Algebra ->  Inequalities -> SOLUTION: I need help with this equation Solve the compound inequality. Then graph the solution 8x 11 < 5 or 4x - 7 > 13      Log On


   

Question 107402This question is from textbook Algebra 1
: I need help with this equation Solve the compound inequality. Then graph the solution
8x 11 < 5 or 4x - 7 > 13 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Does the first one read: 8x+11<5 ?


8x%2B11%3C5 Start with the first inequality


8x%3C5-11Subtract 11 from both sides


8x%3C-6 Combine like terms on the right side


x%3C%28-6%29%2F%288%29 Divide both sides by 8 to isolate x



x%3C-3+%2F+4 Reduce

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Answer:
So the solution set for the first inequality is x%3C-3+%2F+4



Now let's graph the solution set


Set up a number line:
number_line%28500%2C-13%2C7%29

Now plot the point x=-3+%2F+4 on the number line


number_line%28500%2C-13%2C7%2C+-3+%2F+4%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-3+%2F+4


0%3C-3+%2F+4 Plug in x=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point x=-3+%2F+4 as the boundary. This means we shade everything to the left of the point x=-3+%2F+4 like this:
Graph of x%3C-3+%2F+4 with the shaded region in blue

note: at the point x=-3+%2F+4, there is an open circle. This means the point x=-3+%2F+4 is excluded from the solution set.





4x-7%3E13 Now let's move onto the second inequality


4x%3E13%2B7Add 7 to both sides


4x%3E20 Combine like terms on the right side


x%3E%2820%29%2F%284%29 Divide both sides by 4 to isolate x



x%3E5 Divide

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Answer:
So the solution set for the second inequality is x%3E5



Now let's graph the solution set

Set up a number line:
number_line%28500%2C-5%2C15%29

Now plot the point x=5 on the number line


number_line%28500%2C-5%2C15%2C+5%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3E5


0%3E5 Plug in x=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point x=5 as the boundary. This means we shade everything to the right of the point x=5 like this:
Graph of x%3E5 with the shaded region in blue
note: at the point x=5, there is an open circle. This means the point x=5 is excluded from the solution set.



So this means our answer is

x%3C-3%2F4 or x%3E5


So putting the two graphs together gets us: