How do you solve for x in 4-6x \le 2(2x+3)?

1 Answer
Nico Ekkart
Dec 19, 2014

To solve an inequality of the first order (this is one because there isn't a higher exponent of x, than 1), you have to first bring every factor of x to one part, and every number to the other part.

4-6x <= 2(2x+3)
4-6x <= 4x + 6 (apply the distributive property)
4-6x-6 <= 4x+6-6 (substract 6 from both sides)
-2-6x <= 4x
-2-6x+6x <= 4x+6x (add 6x to both sides)
-2 <= 10x
(-2)/10 <= (10x)/10 (divide both sides by ten""^"(1)")
-1/5 <= x
This is your answer, you can flip it if that seams easier:
x >= -1/5
The set of solutions is all the numbers that are greater than or equal to -1/5.

Hope this helped.

(1): If you were to divide by a negative number, you would have to flip the inequality sign. In this case, <= would become >=

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