Absolute value equation examples

What is an absolute value equation?

Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. If the number is negative, then the absolute value is its opposite: |-9|=9. So when we’re dealing with a variable, we need to consider both cases.

How do you solve absolute value equations?

SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)Step 1: Isolate the absolute value expression.Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.Step 3: Solve for the unknown in both equations.Step 4: Check your answer analytically or graphically.

What is a real life example of absolute value?

A geophysicist uses absolute value to look at the total amount of energy used. In an energy wave, there are both negative and positive directions of movement. Another example is when scuba divers discuss their location in regards to sea level. “50 feet below sea level” doesn’t have to be represented as -50 feet.

Is 0 an absolute value?

The absolute value of 0 is 0. (This is why we don’t say that the absolute value of a number is positive: Zero is neither negative nor positive.)

What if an absolute value equation equals zero?

No matter if the number is to the left (negative) or right (positive) of zero on the number line, the DISTANCE it is away from zero is going to be positive. Hence, the absolute value is always positive (or zero if you are taking the absolute value of 0).

How do you simplify absolute value?

Once you have performed any operations inside the absolute value bars, you can simplify the absolute value. Whatever number you have as your argument, whether positive or negative, represents a distance from 0, so your answer is that number, and it is positive. In the example above, the simplified absolute value is 3.

How do I simplify an expression?

Here are the basic steps to follow to simplify an algebraic expression:remove parentheses by multiplying factors.use exponent rules to remove parentheses in terms with exponents.combine like terms by adding coefficients.combine the constants.

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What is absolute value used for?

Absolute values are used when we work with distances. Distances are positive values. For example: A diver is -15 deep (this places him 15 feet below the surface of the water).

What is absolute value graph?

Graphing the Absolute Value Function f (x) = | x| The graph looks like a “V”, with its vertex at (0, 0). Its slope is m = 1 on the right side of the vertex, and m = – 1 on the left side of the vertex. If a < 0, then the greatest y-value for y = a| x - h| + k is y = k.

What is the absolute value definition?

noun Mathematics. Also called numerical value. the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |3| or |−3| is equal to 3.

Is 0 a real number?

Real numbers consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (0.4, 3.1415927, 1/2). Real numbers are divided into rational and irrational numbers.

What is the absolute value of 8?

1 Answer. The absolute value of 8 is 8 .

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