absolute value |a|
the distance between 0 and a on the number line – always positive
Absolute value |a| refers to the distance of a number from the origin, regardless of its sign. In other words, it is the magnitude or size of a number without considering its positive or negative sign. The absolute value of a number is always greater than or equal to zero.
To find the absolute value of a number, we simply remove the negative sign if there is one. For example, the absolute value of -5 is 5, and the absolute value of 7 is 7, as both 5 and 7 are the distances of these numbers from the origin on a number line.
In algebra, absolute value is often used in equations and inequalities. When solving an equation or inequality involving absolute value, we must consider both the positive and negative solutions. For example, the equation |x-3| = 2 has two solutions: x = 1 and x = 5, since both values make the distance between x and 3 equal to 2. Similarly, the inequality |2x+1| > 5 has two solutions: x < -3 or x > 2, since both values make the distance between 2x+1 and the origin greater than 5.
In summary, the absolute value is a mathematical operation that gives the distance of a number from the origin without considering its sign, and it is important in algebraic operations involving equations and inequalities.
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