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Penyelesaian - Absolute value equations

Hasil Akhir Langkah-langkah Terma dan topik

Exact form:

x = \frac{5}{3}, 7

x=\frac{5}{3} , 7

Mixed number form:

x = 1 \frac{2}{3}, 7

x=1\frac{2}{3} , 7

Decimal form:

x = 1.667, 7

x=1.667 , 7

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
$| - 2 x + 6 | = | x + 1 |$
without the absolute value bars:

$\| x \| = \| y \|$	$\| - 2 x + 6 \| = \| x + 1 \|$
$x = + y$	$(- 2 x + 6) = (x + 1)$
$x = - y$	$(- 2 x + 6) = - (x + 1)$
$+ x = y$	$(- 2 x + 6) = (x + 1)$
$- x = y$	$- (- 2 x + 6) = (x + 1)$

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:

$\| x \| = \| y \|$	$\| - 2 x + 6 \| = \| x + 1 \|$
$x = + y$ , $+ x = y$	$(- 2 x + 6) = (x + 1)$
$x = - y$ , $- x = y$	$(- 2 x + 6) = - (x + 1)$

2. Solve the two equations for x

11 additional steps

$(- 2 x + 6) = (x + 1)$

Subtract from both sides:

$(- 2 x + 6) - x = (x + 1) - x$

Kumpulkan sebutan sejenis:

$(- 2 x - x) + 6 = (x + 1) - x$

Permudahkan aritmetik:

$- 3 x + 6 = (x + 1) - x$

Kumpulkan sebutan sejenis:

$- 3 x + 6 = (x - x) + 1$

Permudahkan aritmetik:

$- 3 x + 6 = 1$

Subtract from both sides:

$(- 3 x + 6) - 6 = 1 - 6$

Permudahkan aritmetik:

$- 3 x = 1 - 6$

Permudahkan aritmetik:

$- 3 x = - 5$

Divide both sides by :

$\frac{(- 3 x)}{- 3} = \frac{- 5}{- 3}$

Hapuskan tanda negatif:

$\frac{3 x}{3} = \frac{- 5}{- 3}$

Permudahkan pecahan:

$x = \frac{- 5}{- 3}$

Hapuskan tanda negatif:

$x = \frac{5}{3}$

11 additional steps

$(- 2 x + 6) = - (x + 1)$

Expand the parentheses:

$(- 2 x + 6) = - x - 1$

Add to both sides:

$(- 2 x + 6) + x = (- x - 1) + x$

Kumpulkan sebutan sejenis:

$(- 2 x + x) + 6 = (- x - 1) + x$

Permudahkan aritmetik:

$- x + 6 = (- x - 1) + x$

Kumpulkan sebutan sejenis:

$- x + 6 = (- x + x) - 1$

Permudahkan aritmetik:

$- x + 6 = - 1$

Subtract from both sides:

$(- x + 6) - 6 = - 1 - 6$

Permudahkan aritmetik:

$- x = - 1 - 6$

Permudahkan aritmetik:

$- x = - 7$

Multiply both sides by :

$- x \cdot - 1 = - 7 \cdot - 1$

Buang nilai satu:

$x = - 7 \cdot - 1$

Permudahkan aritmetik:

$x = 7$

3. List the solutions

$x = \frac{5}{3}, 7$
(2 solution(s))

4. Graph

Each line represents the function of one side of the equation:
$y = | - 2 x + 6 |$
$y = | x + 1 |$
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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