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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, 03:26
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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, 03:50
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, 05:00
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, 09:09
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, 15:51
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.
The answer is 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, 18:24
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, 20:28
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

The answer is 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, 21:10
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.

Final answer is (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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30 Nov 2019, 01:41
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, 05:21
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, 05:21
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