How do you solve $abs(a-5)/8=5$ ?

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How do you solve $abs(a-5)/8=5$ ?

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Answer 1 · 2016-08-02T16:50:42

$|a - 5| = 8 xx 5$

We need to consider two separate situations.

a) The absolute value is positive
b) The absolute value is negative

Starting with the positive case:

$a - 5 = 40$

$a = 45$

Now for the negative case:

$-(a - 5) = 40$

$-a + 5 = 40$

$-a = 35$

$a = -35$

Hence, the solution set is ${-35, 45}$ .

Hopefully this helps!

Answer 2 · 2016-08-02T17:03:02

$a= 45" "$ or $" "a = -35$

Explanation:

Absolute value can be negative inside or positive inside. When the value comes out of the absolute value sign it is always positive.

First, multiply both sides by $8$ , the opposite of dividing by $8$ .

$(a- 5)/ 8 xx 8 = 5 xx 8$

Since $8/8= 1$ , you have

$a -5 = 40$

$a-5$ has two possible values. Solve for both values.

$(a-5) = + 40" "$ or $" " a-5 = -40$

$a-5 = + 40 ->$ add $5$ to both sides

$a- cancel(5) + cancel(5) = + 40 + 5$

Since $-5+ 5 = 0$ and $40+5 = +45$ , you have

$a= + 45$

$a-5 = -40 ->$ add $5$ to both sides

$a - cancel(5) + cancel(5) = -40 +5$

Once again, $-5 + 5 = 0$ and $-40 + 5 = -35$

$a = -35$

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How do you solve $abs(a-5)/8=5$ ?

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