How do I solve -26 >6x-8

Question

we are solving inequalities in class and I don't understand tham

Answer 1

Just like equations, inequalities have an expression on each side of the inequality.  To "solve" means to find the value(s) of the variable for which the inequality is true.

 

It is very important to understand the rules for inequalities:

  1. If you add/subtract a value to both sides, then the truth of the inequality is retained.

  2.  If you multiply/divide by a positive value to both sides, the truth of the inequality remains.

  3.  If you multiply/divide by a negative value to both sides, inequality is reversed.

 

"Reversed" means to choose the opposite:

             <   is opposite of    >

             ≤   is opposite of    ≥

 

For this problem, perform the usual algebra operations to isolate x, but follow the rules above.  O.K. let's do it.

       -26 >6x-8                 [given inequality]

       -18 > 6x                 [add positive 8 to both sides; still >]

       -3 > x                    [divide both sides by positive 3; still >]

       x < -3                   [the above expression read right-to-left]

 

You may want to check your answer with an easy value like x=-5 [which is less than -3].

  Is   -26 >6x-8      true?

        -26 > 6(-5) - 8      ?

        -26 > -30 - 8    ?

        -26 > -38   > yes

Answer 2

1.) -26>6x-8 2.) -18>6x 3.) -3>x step 1) add eight to both sides step 2) divide by 6 to isolate the x step 3) x is less that -3