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Penyelesaian - Absolute value equations

Exact form: x=-29,-2
x=-\frac{2}{9} , -2
Decimal form: x=0.222,2
x=-0.222 , -2

Other Ways to Solve

Absolute value equations

Penjelasan langkah demi langkah

1. Rewrite the equation without absolute value bars

Use the rules:
|x|=|y|x=±y and |x|=|y|±x=y
to write all four options of the equation
|3x+2|=|6x+4|
without the absolute value bars:

|x|=|y||3x+2|=|6x+4|
x=+y(3x+2)=(6x+4)
x=y(3x+2)=(6x+4)
+x=y(3x+2)=(6x+4)
x=y(3x+2)=(6x+4)

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||3x+2|=|6x+4|
x=+y , +x=y(3x+2)=(6x+4)
x=y , x=y(3x+2)=(6x+4)

2. Solve the two equations for x

11 additional steps

(-3x+2)=(6x+4)

Subtract from both sides:

(-3x+2)-6x=(6x+4)-6x

Kumpulkan sebutan sejenis:

(-3x-6x)+2=(6x+4)-6x

Permudahkan aritmetik:

-9x+2=(6x+4)-6x

Kumpulkan sebutan sejenis:

-9x+2=(6x-6x)+4

Permudahkan aritmetik:

9x+2=4

Subtract from both sides:

(-9x+2)-2=4-2

Permudahkan aritmetik:

9x=42

Permudahkan aritmetik:

9x=2

Divide both sides by :

(-9x)-9=2-9

Hapuskan tanda negatif:

9x9=2-9

Permudahkan pecahan:

x=2-9

Pindahkan tanda negatif dari penyebut ke pembilang:

x=-29

12 additional steps

(-3x+2)=-(6x+4)

Expand the parentheses:

(-3x+2)=-6x-4

Add to both sides:

(-3x+2)+6x=(-6x-4)+6x

Kumpulkan sebutan sejenis:

(-3x+6x)+2=(-6x-4)+6x

Permudahkan aritmetik:

3x+2=(-6x-4)+6x

Kumpulkan sebutan sejenis:

3x+2=(-6x+6x)-4

Permudahkan aritmetik:

3x+2=4

Subtract from both sides:

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

Permudahkan aritmetik:

3x=42

Permudahkan aritmetik:

3x=6

Divide both sides by :

(3x)3=-63

Permudahkan pecahan:

x=-63

Cari faktor sepunya terbesar bagi pembilang dan penyebut:

x=(-2·3)(1·3)

Faktorkan keluar dan hapuskan faktor sepunya terbesar:

x=2

3. List the solutions

x=-29,-2
(2 solution(s))

4. Graph

Each line represents the function of one side of the equation:
y=|3x+2|
y=|6x+4|
The equation is true where the two lines cross.

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.