|(0) – 1| = 1 to the left side and 2(0) + 1 = 1 to the right. Substituting x by 0 in both sides of the equation results in: Since the two equations are not equal, therefore x = -2 is not an answer to this equation. Substituting x by – 2 in both sides of the expression gives. It is important to check if the solutions are correct for the equation because all the values of x were assumed. One method of solving this equation is to consider two cases:Ī) Assume x – 1 ≥ 0 and rewrite the expression as:ī) Assume x – 1 ≤ 0 and rewrite this expression as The remaining equation is same as to writing the expression as:Ĭalculate the real values to the expression with absolute value.Rewrite the expression with the absolute value sign on one side. Solve the equation by determining absolute values, How far does he need to swim to get to the surface?Ĭalculate the absolute value of 19 – 36(3) + 2(4 – 87)? First of all, start by working out the expressions within the absolute value symbols:Ī sea diver is -20 feet below the surface of the water.Hence, the two possible values of x are -4 and 4. In this equation, 4x can be either positive or negative. Now I can take the negative through the parentheses:.Convert the absolute value symbols to parentheses.Preservation of division |a/b|=|a|/|b| if b ≠ 0.Triangle inequality |a − b| ≤ |a − c| + |c − b|.Identity of indiscernible |a − b| = 0 ⇔ a = b.Properties of Absolute Value Absolute value has the following fundamental properties: The equal sign indicates that all values being compared are included in the graph.Īn easy way of representing expression with inequalities is by following the following rules. This expression is graphed by placing a closed dot on the number line. This includes all absolute values that are less than or equal to 5. This is done graphically by placing an open dot on the number line.Ĭonsider another case where | x| = 5. To represent this, on a number line, you need all numbers whose absolute value is greater than 5. Not only does a number show the distance from the origin, but it also is important for graphing the absolute value.Ĭonsider an expression | x| > 5. This means that distance from 0 is 5 units: Similarly, the absolute value of a negative 5 is denoted as, |-5| = 5. For example, the absolute value of the number 5 is written as, |5| = 5. The absolute value of a number is denoted by two vertical lines enclosing the number or expression. The absolute value of a number is always positive. Absolute Value – Properties & Examples What is an Absolute Value?Ībsolute value refers to a point’s distance from zero or origin on the number line, regardless of the direction.
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