How do you solve $14 + 3 | 2 x - 5 | = 17$ $14+ 3|2x-5| = 17$ ?

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Answer 1 · 2017-09-26T10:13:45

Solution: $x = 3, x = 2$ $x=3 ,x=2$

$14 + 3 | 2 x - 5 | = 17 or 3 | 2 x - 5 | = 17 - 14 or 3 | 2 x - 5 | = 3$ $14 + 3 | 2x-5| =17 or 3 | 2x-5| =17-14 or 3 | 2x-5| =3$

or $| 2 x - 5 | = 1 or 2 x - 5 = 1 or 2 x = 6 or x = 3$ $| 2x-5| =1 or 2x -5 =1 or 2x =6 or x=3$ OR

$14 + 3 | 2 x - 5 | = 17 or 3 | 2 x - 5 | = 17 - 14 or 3 | 2 x - 5 | = 3$ $14 + 3 | 2x-5| =17 or 3 | 2x-5| =17-14 or 3 | 2x-5| =3$

or $| 2 x - 5 | = 1 or 2 x - 5 = - 1 or 2 x = 4 or x = 2$ $| 2x-5| =1 or 2x -5 = -1 or 2x = 4 or x=2$

Solution: $x = 3, x = 2$ $x=3 ,x=2$ [Ans]

Answer 2 · 2017-09-26T10:20:15

$x = 2$ $x = 2$
$x = 3$ $x = 3$

First we would equal the equation to $0$ $0$ be rearranging the equation.

$- 3 + 3 | 2 x - 5 | = 0$ $-3 + 3|2x−5| = 0$

Now for this equation to be complete, we know that $3 | 2 x - 5 |$ $3|2x−5|$ must equal to $3$ $3$ for the equation to equal to $0$ $0$

$3 | 2 x - 5 | = 3$ $3|2x−5| = 3$

Therefore, dividing by 3 on both sides, we get

$| 2 x - 5 | = 1$ $|2x−5| = 1$

Since it is an absolute value we can have two equations

$2 x - 5 = - 1$ $2x−5 = -1$
$2 x - 5 = 1$ $2x−5 = 1$

Rearranging to get $x$ $x$ on its own, we solve for $x$ $x$

$x = \frac{- 1 + 5}{2}$ $x = (-1 + 5)/2$

$x = \frac{1 + 5}{2}$ $x = (1 + 5)/2$

$x = 2$ $x = 2$
$x = 3$ $x = 3$

How do you solve 14+3|2x−5|=1714+ 3|2x-5| = 17?