Question 367035: Hello,
Please help me solve this problem, thank you in advance.
3x + 7 < 4 with x =-.5
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! if x = -.5, then substitute -.5 for x in the equation of 3x + 7 < 4 to get:
3 * (-.5) + 7 < 4
simplify by performing the indicated operations to get:
-1.5 + 7 < 4
simplify by combining like terms to get:
5.5 < 4.
since this is false, x = -.5 does not satisfy the requirements of this equation.
to solve this equation, do the following:
3x + 7 < 4
subtract 7 from both sides of the equation to get:
3x < -3
divide both sides of this equation by 3 to get:
x < -1
x = -.5 is NOT less than -1, so x = -.5 is outside the boundaries of a correct solution to this equation.
to determine if the results of the analysis are accurate, do the following:
pick a value of x > -1
pick a value of x = -1
pick a value of x < -1
x = -.5 is > -1 so that's a good start to show that the equation is false when you use that value, as we found out earlier.
when x = -1, the equation becomes 3*(-1) + 7 < 4
solve this to get -3 + 7 < 4 which becomes 4 < 4 which is not true.
this is good because x = -1 is not smaller than -1 and the result should be false.
pick a value of x < -1.
try x = -1.5 which is smaller than -1.
when x = -1.5, the equation of 3*x + 7 < 4 becomes:
3*(-1.5) + 7 < 4 which becomes -4.5 + 7 < 4 which becomes 2.5 < 4 which is true.
since it should be true because x is smaller than -1, then the answer to your equation is good.
the equation is true when x < -1.
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