{
  "problem": "$B$ is the midpoint of $\\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 2$ and $ BC = 6x - 8$ Find $AC$.",
  "hints": [
    "A midpoint divides a segment into two segments with equal lengths.",
    "${AB} = {BC}$",
    "Substitute in the expressions that were given for each length:",
    "$ {4x - 2} = {6x - 8}$",
    "Solve for",
    "$x$",
    "$ -2x = -6$",
    "$ x = 3$",
    "Substitute",
    "$3$",
    "for",
    "$x$",
    "in the expressions that were given for",
    "$AB$",
    "and",
    "$BC$",
    "$ AB = 4({3}) - 2$",
    "$ BC = 6({3}) - 8$",
    "$ AB = 12 - 2$",
    "$ BC = 18 - 8$",
    "$ AB = 10$",
    "$ BC = 10$",
    "To find the length",
    "$AC$",
    ", add the lengths",
    "${AB}$",
    "and",
    "${BC}$",
    "$ AC = {AB} + {BC}$",
    "$ AC = {10} + {10}$",
    "$ AC = 20$"
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/479/1608153634.json'}