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Penyelesaian - Absolute value equations

Hasil Akhir Langkah-langkah Terma dan topik

Exact form:

x = 2, - 1

x=2 , -1

Lihat langkah Learn more with Tiger Try this:

Penjelasan langkah demi langkah

1. Rewrite the equation without absolute value bars

Use the rules:
$| x | = | y |$ → $x = \pm y$ and $| x | = | y |$ → $\pm x = y$
to write all four options of the equation
$| x + 4 | = | 3 x |$
without the absolute value bars:

$\| x \| = \| y \|$	$\| x + 4 \| = \| 3 x \|$
$x = + y$	$(x + 4) = (3 x)$
$x = - y$	$(x + 4) = - (3 x)$
$+ x = y$	$(x + 4) = (3 x)$
$- x = y$	$- (x + 4) = (3 x)$

When simplified, equations $x = + y$ and $+ x = y$ are the same and equations $x = - y$ and $- x = y$ are the same, so we end up with only 2 equations:

$\| x \| = \| y \|$	$\| x + 4 \| = \| 3 x \|$
$x = + y$ , $+ x = y$	$(x + 4) = (3 x)$
$x = - y$ , $- x = y$	$(x + 4) = - (3 x)$

2. Solve the two equations for x

12 additional steps

$(x + 4) = 3 x$

Subtract from both sides:

$(x + 4) - 3 x = (3 x) - 3 x$

Kumpulkan sebutan sejenis:

$(x - 3 x) + 4 = (3 x) - 3 x$

Permudahkan aritmetik:

$- 2 x + 4 = (3 x) - 3 x$

Permudahkan aritmetik:

$- 2 x + 4 = 0$

Subtract from both sides:

$(- 2 x + 4) - 4 = 0 - 4$

Permudahkan aritmetik:

$- 2 x = 0 - 4$

Permudahkan aritmetik:

$- 2 x = - 4$

Divide both sides by :

$\frac{(- 2 x)}{- 2} = \frac{- 4}{- 2}$

Hapuskan tanda negatif:

$\frac{2 x}{2} = \frac{- 4}{- 2}$

Permudahkan pecahan:

$x = \frac{- 4}{- 2}$

Hapuskan tanda negatif:

$x = \frac{4}{2}$

Cari faktor sepunya terbesar bagi pembilang dan penyebut:

$x = \frac{(2 \cdot 2)}{(1 \cdot 2)}$

Faktorkan keluar dan hapuskan faktor sepunya terbesar:

$x = 2$

8 additional steps

$(x + 4) = - 3 x$

Subtract from both sides:

$(x + 4) - 4 = (- 3 x) - 4$

Permudahkan aritmetik:

$x = (- 3 x) - 4$

Add to both sides:

$x + 3 x = ((- 3 x) - 4) + 3 x$

Permudahkan aritmetik:

$4 x = ((- 3 x) - 4) + 3 x$

Kumpulkan sebutan sejenis:

$4 x = (- 3 x + 3 x) - 4$

Permudahkan aritmetik:

$4 x = - 4$

Divide both sides by :

$\frac{(4 x)}{4} = \frac{- 4}{4}$

Permudahkan pecahan:

$x = \frac{- 4}{4}$

Permudahkan pecahan:

$x = - 1$

3. List the solutions

$x = 2, - 1$
(2 solution(s))

4. Graph

Each line represents the function of one side of the equation:
$y = | x + 4 |$
$y = | 3 x |$
The equation is true where the two lines cross.

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Mengapa belajar ini

Learn more with Tiger

We encounter absolute values almost daily. For example: If you walk 3 miles to school, do you also walk minus 3 miles when you go back home? The answer is no because distances use absolute value. The absolute value of the distance between home and school is 3 miles, there or back.
In short, absolute values help us deal with concepts like distance, ranges of possible values, and deviation from a set value.

Penyelesaian - Absolute value equations

Penjelasan langkah demi langkah

1. Rewrite the equation without absolute value bars

2. Solve the two equations for x

3. List the solutions

4. Graph

Mengapa belajar ini

Terma dan topik

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