Absolute Value Lesson

We indicate absolute value by putting two bars around the number.

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Because the absolute value​ of a number is the distance from zero, it is always positive.

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Absolute Value

​Indicamos el valor absoluto poniendo dos barras alrededor del número. ​

Como el valor absoluto de un número es la distancia desde cero, siempre es positivo.

|9| is read "the absolute value of 9."

Because 9 is 9 spaces from zero on the number line, the absolute value is 9.​

|9| se lee "el valor absoluto de 9."
Como 9 está a 9 espacios del cero en la recta numérica, el valor absoluto es 9.

|9|

|-4| is read "the absolute value of -4."

Because -4 is 4 spaces from zero on the number line, the absolute value is 4.​

|-4| se lee "el valor absoluto de -4".
Como -4 está a 4 espacios de cero en la recta numérica, el valor absoluto es 4.

​|-4|

Absolute Value/Valor absoluto

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

|-20|

• 20
• -20

Multiple Choice

| –3 |

• 3
• -3
• 0.30
• 30

Multiple Choice

What is the absolute value of |-26|

• 26
• -26
• -36
• 36

Absolute value bars are also grouping symbols, so you must complete the operation inside them first, then take the absolute value.​

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​|5-3| = |2| = 2
Las barras de valor absoluto también son símbolos de agrupación, por lo que primero debes completar la operación dentro de ellas y luego tomar el valor absoluto.

Sometimes, there are positive or negative symbols outside an absolute value bar. Think inside, then outside - first take the absolute value of what is inside the bars, then apply the outside symbol.​

-​|6| = -6

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​(The absolute value of 6 is 6. Then we apply the negative symbol on the outside of the absolute value bars to get the answer -6.)

​-​|-16| = -16​

​(The absolute value of -16 is 16. Then we apply the negative symbol on the outside of the absolute value bars to get the answer -16.)

A number in front of the absolute value bars means multiplication (like when we use parentheses).​

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2|-4| (The absolute value of -4 is 4.)

2 x 4 = 8

(Once you have the value inside​ the absolute value bars, you can solve normally.)

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The absolute value of a variable inside the bars can be positive or negative

= 9

The solution to an Absolute value is ALWAYS positive.
If you have to solve for a negative solution there is NO SOLUTION

X=

= -9

How to solve

• Get absolute value by itself

• If equal to a negative the answer is no solution

• If not get rid of absolute value by separating into two two equations

• Solve equations like usual

• Obtener valor absoluto por sí solo

• Si es igual a negativo la respuesta no es solución

• Si no, deshazte del valor absoluto separándolo en dos dos ecuaciones.

• Resuelve ecuaciones como de costumbre.

Example:

Multiple Choice

Solve for x
l 5x l = 40

• x = 8 and x =-8
• x = 35 and x = -35
• Only x = 8
• No Solution

Multiple Choice

| x – 3 |= 0

• 3
• -3
• {-3, 3}
• no solution

Multiple Choice

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

Multiple Choice

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4
• x = 5 and x = -5
• Only x = 5
• No Solution

Example:

Example:

Multiple Choice

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0
• x = 3 and x = -3
• x = -12 and x = 0
• No Solution