How do you solve: 3x-1/6<2?

3x-(1/6)<=2
3x<=13/6
x<=(13/6)/(3)

Ok, if it's (3x - 1)/6 <= 2, here's your answer

Multiplying the whole expression by 6

3x - 1 <= 12

Add 1 to both sides of the expression

3x <= 11

Divide the whole thing by 3

x <= 11/3 <<<< answer.



Now, if it's 3x - 1/6 <= 2

Add 1/6 to both sides:

3x <= 13/6

Divide all by 3

x <= 13/18 <<< Answer.


Good luck! :)

I guess what u mean is (3x -1)/6 < or = 2

(3x -1) <= 2(6) multiply both sides by the multiplicative inverse of 1/6
3x -1 <= 12
3x -1 + 1<=12 +1 by addition property
3x <=13
(3x)(1/3) <= 13(1/3) multiplication property, multiplying both sides by the multiplicative inverse of 3

x <= 13/3

X<(1/6add2)/3

(3x - 1)/6 <= 2
3x - 1 <= 12
3x <= 13
x <= 13/3

The steps are the same as for solving an equality, except for one catch:

If you multiply (or divide) both sides by a negative number, the inequality flips direction.

Example:
3 < 5 (three is smaller than 5)
multiply by -1 on both sides:

-3 > -5 (minus 3 is greater than -5)
the direction of the inequality "flipped" because we multiplied by a negative number.

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Let's say you started with 3x - (1/6) < 2
add (1/6) to both sides
3x - (1/6) + (1/6) < 2 + (1/6)
3x < 13/6
divide both sides by +3 (when multiplying and dividing, it is good to show the sign, in order to avoid confusion)
Dividing by a positive number: the inequality does not flip.

3x / 3 < (13/6) / 3
x < 13/18

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You can do the same type of approach with
(3x-1)/6 < 2
first step, multiply both sides by +6 (positive: the inequality does not flip)

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The rule about flipping the inequality only applies to multiplication or division, it does not apply for addition or subtraction.

If you are not certain, do a little test on the side:

-3 > -5
subtract 7 from both sides

-3 - 7 > -5 - 7
-10 > -12
still true; subtracting 7 did not flip the inequality

3x - 1/6 ≤ 2
3x ≤ 2 + 1/6
3x ≤ 12/6 + 1/6
3x ≤ 13/6
x ≤ (13/6)/3
x ≤ (13/6)(1/3)
x ≤ 13/18

3x - 1/6 <= 2

Add 1/6 to both sides
3x - 1/6 + 1/6 <= 2 + 1/6
3x + 0 <= 12/6 + 1/6
3x <= 13/6

Divide both sides by 3
3x / 3 <= (13/6) / 3
x <= (13/6) / 3
x <= 13/18

:)

3x -(1/6) LTE 2 (LTE means 'less than or eqaul to')
3x LTE 2 + 1/6

3x LTE 12/6+1/6
3x LTE 13/6 (now divide by 3 to islate x)

x LTE 13/6 times 1/3

x LTE 13/18