<\/span><\/h3>\nThe distance between any two points on a number line can be found by taking the absolute value of the difference between those points.<\/p>\n
For example, if two points are given as A and B, the distance between them (d) is given by the formula:
\nd = |A – B|<\/p>\n
Let’s go through a step-by-step example to make it clearer.<\/p>\n
Example: Solve the absolute value equation |2x + 3| = 7 and find the distance.<\/p>\n
Step 1: Isolate the absolute value expression:
\n2x + 3 = 7 or 2x + 3 = -7<\/p>\n
Step 2: Set up two equations:
\n2x + 3 = 7
\n2x + 3 = -7<\/p>\n
Step 3: Solve each equation separately:
\nFor the first equation, we have:
\n2x = 4
\nx = 2<\/p>\n
For the second equation, we have:
\n2x = -10
\nx = -5<\/p>\n
Step 4: Check your solutions:
\nSubstituting x = 2 into the original equation |2x + 3| = 7:
\n|2(2) + 3| = 7
\n|4 + 3| = 7
\n|7| = 7
\n7 = 7 (LHS = RHS)<\/p>\n
Substituting x = -5 into the original equation |2x + 3| = 7:
\n|2(-5) + 3| = 7
\n|-10 + 3| = 7
\n|-7| = 7
\n7 = 7 (LHS = RHS)<\/p>\n
Both solutions are correct.<\/p>\n
Step 5: Answer
\nThe solutions to the equation |2x + 3| = 7 are x = 2 and x = -5. The distance between these two points is:
\nd = |2 – (-5)|
\nd = 7<\/p>\n
Therefore, the distance between the two points is 7 units.<\/p>\n