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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

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