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# If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value

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If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 02:26
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If $$y = |6x - 18| + |-7x + 7| + |3x + 2|$$, for what x-value is the value of y minimized?

A. $$-\frac{2}{3}$$
B. 1
C. 2
D. 3
E. $$\frac{7}{2}$$

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 02:50
1
value of y=|6x−18|+|−7x+7|+|3x+2| is minimised at x= 1 ; y = 17
IMO B

If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. −23−23
B. 1
C. 2
D. 3
E. 7272
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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 04:00
1
Quote:
If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. −2/3
B. 1
C. 2
D. 3
E. 7/2

Replace each answer choice into y=|6x−18|+|−7x+7|+|3x+2| and the least value of y is when x=1.

Ans (B)
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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 08:09
1
From options

A. -2/3.....33+
B. 1........17........ correct
C. 2........21
D. 3........25
E. 7/2......28+

OA:B

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 14:51
1
|6x —18|+ |—7x+7|+ |3x+2| Is always greater than zero(inclusive)

—> the minimum value of y could be 0, if 6x—18=0, —7x+7=0, and 3x+2=0 at the same time.
—> we have to check the values of y ( if x=3, x= 1, and x= —2/3)
y(3)= 0+ 14+ 11= 25
y(1)= 12+ 0+ 5= 17
y(—2/3)= 22+ 35/3+ 0= 101/3

Minimum value of y should be 17, if x is equal to 1.

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 17:24
1
If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value of y minimized?

We can substitute and check for which value of x from the option is the value of y least.

—> y = 6|x - 3| + 7|-x + 1| + |3x + 2|

A. -2/3 ; y = 6|-2/3 - 3| + 7|-(-2/3) + 1| + |3(-2/3) + 2| = 22 + 35/3 = 101/3

B. 1 ; y = 6|1 - 3| + 7|-1 + 1| + |3(1) + 2| = 12 + 0 + 5 = 17

C. 2 ; y = 6|2 - 3| + 7|-2 + 1| + |3(2) + 2| = 6 + 7 + 8 = 21

D. 3 ; y = 6|3 - 3| + 7|-3 + 1| + |3(3) + 2| = 0 + 14 + 11 = 25

E. 7/2 ; y = 6|7/2 - 3| + 7|-7/2 + 1| + |3(7/2) + 2| = 3 + 35/2 + 25/2 = 33

Least value of y is 17, when x = 1

IMO Option B

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 19:28
2
y=|6x-18|+|7-7x|+|3x+2|
when x=-2/3
y=22+35/3+0=33+2/3
when x=1
y=12+5=17
when x=2
y=6+7+8=21
when x=3
y=14+11=25
Obviously, we can see that x=3.5 will yield a much larger value that x=3 since we can see a trend whereby when x increases, y also increases.
when x=3.5
y=3+17.5+12.5=31
The least value out of the options is when x=1

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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29 Nov 2019, 20:10
1
Fastest and surest way to do this is to plug-in numbers (from choices) to the equation and see any inflection point among x values.

y = |6x - 18| + |-7x + 7| + |3x + 2|

A. x=-2/3 --> y= 22 + 2.3 + 0 = 24.3

B. x=1 --> y= 12 + 0 + 5 = 17

C. x=2 --> y= 6 + 7 + 8 = 21

D. x=3 --> y= 0 + 14 + 11

E. x=3.5 --> y= 3 + 17.5 + 12.5

For this question, we just need to calculate choices (A),(B),(C). We see clear inflection point at choice (B).. Calculation on choices (D) and (E) is shown for clarity purpose only.

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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30 Nov 2019, 00:41
1
If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. -$$\frac{2}{3}$$
B. 1
C. 2
D. 3
E. $$\frac{7}{2}$$

Here x > 3 or x < 3 OR x > 1 or x < 1 OR x > -$$\frac{2}{3}$$ or x < -$$\frac{2}{3}$$
Since y is sum of absolute values we have to find its least possible positive value which would be possible for only one value of x.

Checking for each value -
x = -$$\frac{2}{3}$$, y = 24
x = 1, y = 17
x = 2, y = 21
x = 3, y = 25
x = $$\frac{7}{2}$$, y = 33

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Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

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09 Dec 2019, 04:21
1
Greatest coefficient of X is 7. So how can we minimize that term. We'd easily land up with 1 which makes that 0.
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value   [#permalink] 09 Dec 2019, 04:21
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