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Penyelesaian - Absolute value equations

Hasil Akhir Langkah-langkah Terma dan topik

Exact form:

x = - \frac{1}{2}, - \frac{7}{4}

x=-\frac{1}{2} , -\frac{7}{4}

Mixed number form:

x = - \frac{1}{2}, - 1 \frac{3}{4}

x=-\frac{1}{2} , -1\frac{3}{4}

Decimal form:

x = - 0.5, - 1.75

x=-0.5 , -1.75

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
$| - 3 x - 4 | = | - x - 3 |$
without the absolute value bars:

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

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:

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

2. Solve the two equations for x

11 additional steps

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

Add to both sides:

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

Kumpulkan sebutan sejenis:

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

Permudahkan aritmetik:

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

Kumpulkan sebutan sejenis:

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

Permudahkan aritmetik:

$- 2 x - 4 = - 3$

Add to both sides:

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

Permudahkan aritmetik:

$- 2 x = - 3 + 4$

Permudahkan aritmetik:

$- 2 x = 1$

Divide both sides by :

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

Hapuskan tanda negatif:

$\frac{2 x}{2} = \frac{1}{- 2}$

Permudahkan pecahan:

$x = \frac{1}{- 2}$

Pindahkan tanda negatif dari penyebut ke pembilang:

$x = \frac{- 1}{2}$

12 additional steps

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

Expand the parentheses:

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

Subtract from both sides:

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

Kumpulkan sebutan sejenis:

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

Permudahkan aritmetik:

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

Kumpulkan sebutan sejenis:

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

Permudahkan aritmetik:

$- 4 x - 4 = 3$

Add to both sides:

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

Permudahkan aritmetik:

$- 4 x = 3 + 4$

Permudahkan aritmetik:

$- 4 x = 7$

Divide both sides by :

$\frac{(- 4 x)}{- 4} = \frac{7}{- 4}$

Hapuskan tanda negatif:

$\frac{4 x}{4} = \frac{7}{- 4}$

Permudahkan pecahan:

$x = \frac{7}{- 4}$

Pindahkan tanda negatif dari penyebut ke pembilang:

$x = \frac{- 7}{4}$

3. List the solutions

$x = - \frac{1}{2}, - \frac{7}{4}$
(2 solution(s))

4. Graph

Each line represents the function of one side of the equation:
$y = | - 3 x - 4 |$
$y = | - x - 3 |$
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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