Question

Hey Mates

Solve the Following

Find the Number Of Solutions Of the Following

$|x - 1| + |x - 2| + |x - 3| = 9$
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Answer 1

Answer:

Step-by-step explanation:

hope it really helps

Answer 2

$\huge\star{\underline{\tt{\red{\boxed{Answer \implies 2\: Solutions}}}}}\star$

$\huge\bold{\purple{\mathscr{Explanation:}}}$

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Here there are 3 modulus in the equation given above

$\implies$ Four cases will be Taken

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$\bigcirc$ x<1

$\bigcirc$ 1≤x<2

$\bigcirc$ 2≤x<3

$\bigcirc$ x≥3

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|x-1| + |x-2| + |x-3| = 9

$\bigcirc$ For x<1

$\implies$All Modulus Will be Opened With a negative sign

$\implies$-x+1-x+2-x+3=9

-3x+6=9

-3x=3

$\implies$x=-1

here x<1

$\blacksquare$-1 is a solution✓

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$\bigcirc$ 1≤x<2

$\implies$2nd and 3rd Modulus will be negative

$\implies$x-1-x+2-x+3=9

x+4=9

$\implies$x=-5

here x is not the solution

$\blacksquare$x≠-5

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$\bigcirc$2≤x<3

$\implies$ Only 3rd modulus Will be Negative

$\implies$x-1+x-2-x+3=9

$\implies$x=9

here x is not the solution

$\blacksquare$x≠9

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$\bigcirc$x≥3

$\implies$All Modulus Will Be Positive

$\implies$ x-1+x-2+x-3=9

3x-6=9

3x=15

$\implies$x=5

here x≥3

$\blacksquare$5 is a solution✓

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