How do you solve $| 4 x - 2 | = | - x + 5 |$ $|4x - 2| = | - x + 5|$ ?

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How do you solve $| 4 x - 2 | = | - x + 5 |$ $|4x - 2| = | - x + 5|$ ?

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Answer 1 · 2018-04-02T16:38:39

The solutions are $S = {- 1, \frac{7}{5}}$ $S={-1, 7/5}$

Explanation:

Let's build a sign chart

$a a a a$ $color(white)(aaaa)$ $x$ $x$ $a a a a a a a$ $color(white)(aaaaaaa)$ $- \infty$ $-oo$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $\frac{1}{2}$ $1/2$ $a a a a a a a a a a$ $color(white)(aaaaaaaaaa)$ $5$ $5$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $+ \infty$ $+oo$

$a a a a$ $color(white)(aaaa)$ $4 x - 2$ $4x-2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $-$ $-$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $+$ $+$

$a a a a$ $color(white)(aaaa)$ $- x + 5$ $-x+5$ $a a a a a a$ $color(white)(aaaaaa)$ $+$ $+$ $a a$ $color(white)(aa)$ #color(white)(aaaaaaaaa)+# $a a a a a$ $color(white)(aaaaa)$ $0$ $0$ $a a a$ $color(white)(aaa)$ $-$ $-$

$a a a a$ $color(white)(aaaa)$ $| 4 x - 2 |$ $|4x-2|$ $a a a a a a$ $color(white)(aaaaaa)$ $- 4 x + 2$ $-4x+2$ $a a$ $color(white)(aa)$ #color(white)(aaaa)4x-2# $a a a a a$ $color(white)(aaaaa)$ $4 x - 2$ $4x-2$

$a a a a$ $color(white)(aaaa)$ $| - x + 5 |$ $|-x+5|$ $a a a a a a a$ $color(white)(aaaaaaa)$ $x - 5$ $x-5$ $a a$ $color(white)(aa)$ #color(white)(aaaa)x-5# $a a a a a$ $color(white)(aaaaa)$ $- x + 5$ $-x+5$

Therefore,

In the interval $x \in (- \infty, \frac{1}{2})$ $x in (-oo, 1/2)$

$- 4 x + 2 = x - 5$ $-4x+2=x-5$

$5 x = 7$ $5x=7$

$x = \frac{7}{5}$ $x=7/5$

In the interval $x \in (\frac{1}{2}, 5)$ $x in (1/2, 5)$

$4 x - 2 = x - 5$ $4x-2=x-5$

$3 x = - 3$ $3x=-3$

$x = - 1$ $x=-1$

In the interval $x \in (5, + \infty)$ $x in (5, +oo)$

$4 x - 2 = - x + 5$ $4x-2=-x+5$

$5 x = 7$ $5x=7$

$x = \frac{7}{5}$ $x=7/5$

Therefore,

the solutions are $S = {- 1, \frac{7}{5}}$ $S={-1, 7/5}$

graph{(y-|4x-2|)(y-|-x+5|)=0 [-7.11, 8.69, -0.55, 7.35]}

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How do you solve $| 4 x - 2 | = | - x + 5 |$ $|4x - 2| = | - x + 5|$ ?

1 Answer

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