Answered

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Solve the following equation:
30= |- 4y + 2|

Sagot :

Suppose [tex]-4y+2\ge0[/tex]. Then by definition of absolute value,

[tex]|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}[/tex]

On the other hand, suppose [tex]-4y+2<0[/tex]. Then

[tex]|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}[/tex]

Recall the definition,

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

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