Question 1108052
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.