Question

Tentukan himpunan penyelesaian dari persamaan nilai mutlak di bawah ini:

Answer 1

Persamaan Nilai Mutlak

[tex]\sf 2|x-5|+7=13\\\\2|x-5|=13-7\\\\2|x-5|=6\\\\\frac{2|x-5|}{2} =\frac{6}{2} \\\\|x-5|=3\\\\-(x-5)=3\:\:\:atau\:\:\:x-5=3\\\\x-5=-3\:\:\:atau\:\:\:x-5=3\\\\x=-3+5\:\:\:atau\:\:\:x=3+5\\\\x=2\:\:\:atau\:\:\:x=8[/tex]

∴ HP = {x = 2 atau x = 8}

Answer 2

Nilai Mutlak

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Diberikan

• [tex]2|x - 5|+7 = 13[/tex]

Tentukan

• [tex]\texttt{Himpunan penyelesaian}[/tex]

Hasil dan Perhitungan

Sederhanakan Nilai Mutlak tersebut

[tex]2|x - 5|+7 = 13[/tex]

[tex]~~~~~~~2|x - 5|= 13 - 7[/tex]

[tex]~~~~~~~2|x - 5|= 6[/tex]

[tex]~~~~~~~~~|x - 5|= \frac{6}{2} [/tex]

[tex]~~~~~~~~~|x - 5|= 3[/tex]

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Selesaikan Persamaan-Persamaan

[tex]\begin{array}{lr}x - 5 = 3 \\ x - 5 = - 3 \end{array}[/tex]

[tex]\begin{array}{lr}x_{1} = 3 + 5 \\ x_{2} = - 3 + 5 \end{array}[/tex]

[tex]\boxed{\begin{array}{lr}x_{1} = 8 \\ x_{2} = 2 \end{array}}[/tex]

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[tex]\boxed{\colorbox{ccddff}{\texttt{Answered by Danial Alf'at}}} \texttt{ 09-03-2023}[/tex]