Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

The number of the integral solution of $\left | 5x+7 \right |+\left |2x-14 \right |=21$ is
Option: 1
2

Option: 2
3

Option: 3
1

Option: 4
0

Answers (1)

best_answer

$\left | 5x+7 \right |+\left |2x-14 \right |=21$

Case 1:

$5x+7\geq 0$ and $2x-14 \geq 0$

i.e. $x\geq 7$

Both mod signs open with the positive sign

$(5x+7 )+(2x-14) =21$

$7x-7 =21$

$x=4$

but $x\geq7$
Hence no answer in this interval

Case 2:

$5x+7\leq 0$ and $2x-14 \leq 0$

i.e. $x\leq -\frac{7}{5}$

Both mod signs open with a negative sign

$-(5x+7 )-(2x-14) =21$

$-7x+7 =21$

$x=-2$ and $x\leq -\frac{7}{5}$
Hence $x=-2$ is one solution

Case 3:

$5x+7\leq 0$ and $2x-14 \geq 0$

i.e. $x\leq -\frac{7}{5}$ and $x \geq 7$

Not possible

Case 4:

$5x+7\geq 0$ and $2x-14 \leq 0$

i.e. $x\geq -\frac{7}{5}$ and $x \leq 7$

$5x+7$ open with the positive sign and $2x-14$ with the negative sign

$(5x+7 )-(2x-14) =21$

$3x+21 =21$

$x=0$ and $-\frac{7}{5}\leq x \leq7$
Hence $x=0$ is another solution

Total number of integral solution is 2

Posted by

Ajit Kumar Dubey

View full answer

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Latest Question