-2 x -3 y -15-12 xB- -5-4 x - y -5-4 xC- 5-4 x-y-5-4 xD- 5-4 x - y -5-4 x

The correct option is B 5 4x lt; y lt; 5 4xLets look at the given inequality |12x + 3y| lt;15 We know that if |x| lt;a, then a lt;x lt;a ...

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Byju's Answer

Standard XII

Mathematics

Application of inequalities and absolute values

|2 x +3 y |15...

Question

$| 2 x + 3 y | < 15$ What is the range of values for y, expressed in terms of x?

y > 15 - 12 x

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- 5 - 4 x < y < 5 - 4 x

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5 + 4 x < y < 5 - 4 x

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5 - 4 x < y < 5 + 4 x

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Solution

The correct option is B $- 5 - 4 x < y < 5 - 4 x$
Lets look at the given inequality
$| 12 x + 3 y | < 15$
We know that if $| x | < a$ , then $- a < x < a$
Therefore, $| 12 x + 3 y | < 15$
$- 15 < 12 x + 3 y < 15$

Subtract 12x from each side
$- 15 - 12 x < 12 x + 3 y - 12 x < 15 - 12 x$
$- 15 - 12 x < 3 y < 15 - 12 x$

Divide by 3 on each side
$\frac{- 15 - 12 x}{3} < \frac{3 y}{3} < \frac{15 - 12 x}{3}$
$- 5 - 4 x < y < 5 - 4 x$

Correct answer is option B.

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Similar questions

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Q. If 5y − 3x + 15 = 0, then express y in terms of x.

For the equation, $x + 3 y = 5$ , $x$ in terms of $y$ can be written as____ and $y$ in terms of $x$ can be written as ______.

Q. I. For the equation x + 3y = 5, Write the expression y in terms of x .
II. Find the value of y at x = 2 .

Q. Find the value of y in terms of x:

2 x + 3 y + 5 = 0

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|2x+3y|<15 What is the range of values for y, expressed in terms of x?

$| 2 x + 3 y | < 15$ What is the range of values for y, expressed in terms of x?