{
  "problem": "$\\dfrac{ 9q + 9r }{ -6 } = \\dfrac{ 3q - 7s }{ -5 }$ Solve for $q$.",
  "hints": [
    "Multiply both sides by the left denominator.",
    "$\\dfrac{ 9q + 9r }{ -{6} } = \\dfrac{ 3q - 7s }{ -5 }$",
    "$-{6} \\cdot \\dfrac{ 9q + 9r }{ -{6} } = -{6} \\cdot \\dfrac{ 3q - 7s }{ -5 }$",
    "$9q + 9r = -{6} \\cdot \\dfrac { 3q - 7s }{ -5 }$",
    "Multiply both sides by the right denominator.",
    "$9q + 9r = -6 \\cdot \\dfrac{ 3q - 7s }{ -{5} }$",
    "$-{5} \\cdot \\left( 9q + 9r \\right) = -{5} \\cdot -6 \\cdot \\dfrac{ 3q - 7s }{ -{5} }$",
    "$-{5} \\cdot \\left( 9q + 9r \\right) = -6 \\cdot \\left( 3q - 7s \\right)$",
    "Distribute",
    "both sides",
    "$-{5} \\cdot \\left( 9q + 9r \\right) = -{6} \\cdot \\left( 3q - 7s \\right)$",
    "$-{45}q - {45}r = -{18}q + {42}s$",
    "Combine",
    "$q$",
    "terms on the left.",
    "$-{45q} - 45r = -{18q} + 42s$",
    "$-{27q} - 45r = 42s$",
    "Move the",
    "$r$",
    "term to the right.",
    "$-27q - {45r} = 42s$",
    "$-27q = 42s + {45r}$",
    "Isolate",
    "$q$",
    "by dividing both sides by its coefficient.",
    "$-{27}q = 42s + 45r$",
    "$q = \\dfrac{ 42s + 45r }{ -{27} }$",
    "All of these terms are divisible by",
    "$3$",
    "Divide by the common factor and swap signs so the denominator isn't negative.",
    "$q = \\dfrac{ -{14}s - {15}r }{ {9} }$"
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/323/1608104699.json'}