Question 1108052: Find the correct solution set that satisfies the inequality
5x+2≥7(x+2)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 5x + 2 >= 7 * (x + 2)
simplify to get 5x + 2 >= 7x + 14
subtract 5x from both sides of the equation and subtract 14 from both sides of the equation to get 2 - 14 >= 7x - 5x.
combine like terms to get -12 >= 2x
divide both sides of the equation by 2 to get -6 >= x
this is the same as x <= -6.
that's your solution.
you could also have solved it this way:
start with 5x + 2 >= 7x + 14
subtract 7x from both sides of the equation and subtract 2 from both sides of the equation to get 5x - 7x >= 14 - 2
combine like terms to get -2x >= 12
divide both sides of the equation by -2 to get x <= -6.
note that multiplying or dividing both sides of an inequality reverses the inequality.
example:
5 > 3
multiply both sides by -1 gets you -5 < -3
since division is just another form of multiplication, it works for division as well.
example:
10 < 20
divide both sides by -2 gets you -5 > -10
division by -2 is the same as multiplication by -1/2
10 < 20
multiply both sides by -1/2 gets you -5 > -10.
anyway, back to the problem at hand.
your solution is the x <= -6.
to confirm replace x in the original equation with -8, -6, -4.
original equation is 5x + 2 >= 7 * (x + 2)
when x = -8, this becomes -38 >= -42 which is true.
when x = -6, this becomes -28 >= -28 which is true.
when x = -4, this becomes -18 >= -14 which is false.
solution is confirmed to be good because, when x <=-6, the original equation is true, and when x > -6, the original equation is false.
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