SOLUTION: Hello, Please help me solve this problem, thank you in advance. 3x + 7

SOLUTION: Hello, Please help me solve this problem, thank you in advance. 3x + 7 < 4 with x =-.5

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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