How do you solve 3abs(2x-5)=39?

May 24, 2018

x=-4 or x=9

Explanation:

lets find first where $2 x - 5 = 0$ the answer to that is $x = 2.5$
If $x > 2.5$ then $2 x - 5 > 0$ so the ansolute value is $3 \left(2 x - 5\right) = 39$
If $x < 2.5$ then $2 x - 5 < 0$ so the absolute value is $3 \left(5 - 2 x\right) = 39$
So it gives u different solutions in the first case where the $x > 2.5$ is $6 x - 15 = 39 \implies 6 x = 54 \implies x = 9$
In the secont case where $x < 2.5 i t s 15 - 6 x = 39 \implies 6 x = - 24 \implies x = - 4$

May 24, 2018

$x = 9 \mathmr{and} x = - 4$

Explanation:

Well, we can divide the $3$ out to get

|2x−5|=13

Now we know that $2 x - 5$ must equal $13$ or $- 13$ because it is the absolute value. We set $2 x - 5$ equal to $13$ and $- 13$ and solve for $x$.

So

$2 x - 5 + 5 = 13 + 5$

$2 x = 18$

Divide both sides by $2$ and get

$x = 9$

Also

$2 x - 5 + 5 = - 13 + 5$

$2 x = - 8$

Divide both sides by $2$ and get

$x = - 4$

There you have it. $x = 9$ or $x = - 4$.