MHB What is the solution to 1-(x-3)/3 ≤ 1/2?

[alg]

View attachment 9583

 

[skeeter]

$1 - \dfrac{x-3}{3} \le \dfrac{1}{2}$

multiply every term by the common denominator, $6$ ...

$6 - 2(x-3) \le 3$

can you finish it?

 

[alg]

Yes, thank you

-2x - 6 ≤ -3
-2x ≤ -9
x ≤ 9/2

 

[skeeter]

Yes, thank you

-2x - 6 ≤ -3
-2x ≤ -9
x ≤ 9/2

... what happens when you divide both sides of an inequality by a negative number ?

 

[HallsofIvy]

Yes, thank you

-2x - 6 ≤ -3
-2x ≤ -9
x ≤ 9/2

If x= -2 then x is certainly less than 9/2= 4 but -2x- 6= 4- 6= -2 is not less than -3 so that can't be right.

 

[alg]

Correction

6 - 2(x - 3) ≤ 3
-2x - 6 ≤ -3
-2x ≤ -3
flip inequality sign
x ≥ 3/2

 

[skeeter]

Correction

6 - 2(x - 3) ≤ 3
-2x - 6 ≤ -3 should be -2x + 6 < -3
-2x ≤ -3
flip inequality sign
x ≥ 3/2

correction again