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Solve 1-(x-3)/3⩽1/2

frctl

New member
Feb 28, 2020
6
Screen Shot 2020-03-04 at 10.06.09 AM.png
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
613
North Texas
$1 - \dfrac{x-3}{3} \le \dfrac{1}{2}$

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

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

can you finish it?
 

frctl

New member
Feb 28, 2020
6
Yes, thank you

-2x - 6 ≤ -3
-2x ≤ -9
x ≤ 9/2
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
613
North Texas
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

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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.
 

frctl

New member
Feb 28, 2020
6
Correction

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

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
613
North Texas
Correction

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

correction again