SOLUTION: Can anybody here please show me how solve and graph the solution on the number line?
2(2 - 3x) <= 4(x + 1)
Thanks.
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-> SOLUTION: Can anybody here please show me how solve and graph the solution on the number line?
2(2 - 3x) <= 4(x + 1)
Thanks.
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Question 159075: Can anybody here please show me how solve and graph the solution on the number line?
2(2 - 3x) <= 4(x + 1)
Thanks. Found 2 solutions by gonzo, Edwin McCravy:Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! it appears the solution is x <= 0
here's how i solved it algebraically.
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problems states 2*(2-3*x) <= 4*(x+1)
solving for x, the equation becomes
4 - (6*x) <= (4*x) + 4 which becomes
-6*x + 4 <= 4*x + 4
subtract 4 from both sides of the equation to get
-6*x <= 4*x
add (-6*x) to both sides of the equation to get
0 <= 10*x
divide both sides of the equation by 10 to get
0 <= x
subtract x from both sides of the equation to get
-x <= 0
multiply both sides of the equation by (-1) to get
x >= 0
note the reverse in the inequality when you multiply both sides by -1. smaller then becomes greater then.
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the equation appears to be satisfied when x >= 0.
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to create graphs of these equations, set
y = -6*x + 4 for one of these equation, and set
y = 4*x + 4 for the other equation.
graph both equations from x = -3 to x = +3, and from y = - 12 to y = +12.
when viewing the graph, the line ascending (getting higher) from left to right will be the line for the equation y = 4*x + 1. the line descending (getting lower) from left to right will be the line for the equation y = -6*x + 4
from the graph you can see that when x = 0, y = 4 for both equations which represents the equality.
when x > 0, the y value for (-6*x + 4) is less then the y value for (4*x + 1) which supports the conclusion that -6*x + 1 <= 4*x + 1 when x >= 0.
Can anybody here please show me how solve and graph the solution on the number line?
Distribute to remove the parentheses:
Add to both sides:
Add to both sides:
Divide both sides by which
requires that the inequality symbol be reversed:
On a number line that means to shade the number
line including 0 and everything to the right of 0:
----------------@===============>
-5 -4 -3 -2 -1 0 1 2 3 4 5
The interval notation abbreviation for that is
Edwin
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