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Penyelesaian - Absolute value equations

Hasil Akhir Langkah-langkah Terma dan topik

Exact form:

y = 12, - 12

y=12 , -12

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
$| y - 12 | = | - y + 12 |$
without the absolute value bars:

$\| x \| = \| y \|$	$\| y - 12 \| = \| - y + 12 \|$
$x = + y$	$(y - 12) = (- y + 12)$
$x = - y$	$(y - 12) = - (- y + 12)$
$+ x = y$	$(y - 12) = (- y + 12)$
$- x = y$	$- (y - 12) = (- y + 12)$

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:

$\| x \| = \| y \|$	$\| y - 12 \| = \| - y + 12 \|$
$x = + y$ , $+ x = y$	$(y - 12) = (- y + 12)$
$x = - y$ , $- x = y$	$(y - 12) = - (- y + 12)$

2. Solve the two equations for y

11 additional steps

$(y - 12) = (- y + 12)$

Add to both sides:

$(y - 12) + y = (- y + 12) + y$

Kumpulkan sebutan sejenis:

$(y + y) - 12 = (- y + 12) + y$

Permudahkan aritmetik:

$2 y - 12 = (- y + 12) + y$

Kumpulkan sebutan sejenis:

$2 y - 12 = (- y + y) + 12$

Permudahkan aritmetik:

$2 y - 12 = 12$

Add to both sides:

$(2 y - 12) + 12 = 12 + 12$

Permudahkan aritmetik:

$2 y = 12 + 12$

Permudahkan aritmetik:

$2 y = 24$

Divide both sides by :

$\frac{(2 y)}{2} = \frac{24}{2}$

Permudahkan pecahan:

$y = \frac{24}{2}$

Cari faktor sepunya terbesar bagi pembilang dan penyebut:

$y = \frac{(12 \cdot 2)}{(1 \cdot 2)}$

Faktorkan keluar dan hapuskan faktor sepunya terbesar:

$y = 12$

5 additional steps

$(y - 12) = - (- y + 12)$

Expand the parentheses:

$(y - 12) = y - 12$

Subtract from both sides:

$(y - 12) - y = (y - 12) - y$

Kumpulkan sebutan sejenis:

$(y - y) - 12 = (y - 12) - y$

Permudahkan aritmetik:

$- 12 = (y - 12) - y$

Kumpulkan sebutan sejenis:

$- 12 = (y - y) - 12$

Permudahkan aritmetik:

$- 12 = - 12$

3. List the solutions

$y = 12, - 12$
(2 solution(s))

4. Graph

Each line represents the function of one side of the equation:
$y = | y - 12 |$
$y = | - y + 12 |$
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 y

3. List the solutions

4. Graph

Mengapa belajar ini

Terma dan topik

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