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Determine the solutions of the equation:

Absolute value of the quantity one fifth times x plus 2 end quantity minus 6 equals two.

x = −50 and x = 30
x = −30 and x = 50
x = −20 and x = 50
x = 30 and x = 10



Answer :

semsee45

Answer:

x = -50 and x = 30

Step-by-step explanation:

Given equation:

[tex]\left|\dfrac{1}{5}x+2\right|-6=2[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies \left|\dfrac{1}{5}x+2\right|-6+6=2+6[/tex]

[tex]\implies \left|\dfrac{1}{5}x+2\right|=8[/tex]

Set the contents of the absolute value equal to both the negative and positive value of the number on the other side of the equation, then solve both equations:

Equation 1 (negative value)

[tex]\begin{aligned} \dfrac{1}{5}x+2&=-8\\ \dfrac{1}{5}x+2-2&=-8 -2\\\dfrac{1}{5}x&=-10\\ 5 \cdot \dfrac{1}{5}x&=5 \cdot-10\\ x & = -50\end{aligned}[/tex]

Equation 2 (positive value)

[tex]\begin{aligned} \dfrac{1}{5}x+2&=8\\ \dfrac{1}{5}x+2-2&=8 -2\\\dfrac{1}{5}x&=6\\ 5 \cdot \dfrac{1}{5}x&=5 \cdot6\\ x & = 30\end{aligned}[/tex]

Therefore, the solutions are

  • x = -50 and x = 30

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