Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-7(3x-\frac{2}{3})=-8x+\frac{8}{11}\)
  2. \(3(3x-\frac{3}{8})=-4x+\frac{4}{7}\)
  3. \(-3(-4x-\frac{4}{5})=7x+\frac{8}{11}\)
  4. \(5(-5x-\frac{5}{6})=6x+\frac{4}{5}\)
  5. \(2(2x-\frac{2}{5})=9x+\frac{8}{7}\)
  6. \(-6(-3x-\frac{5}{11})=5x+\frac{10}{9}\)
  7. \(5(-5x-\frac{5}{11})=7x+\frac{5}{12}\)
  8. \(-4(-3x-\frac{2}{3})=5x+\frac{4}{9}\)
  9. \(4(5x-\frac{5}{3})=-7x+\frac{4}{11}\)
  10. \(5(-5x+\frac{2}{3})=-2x+\frac{4}{3}\)
  11. \(2(-3x-\frac{4}{7})=7x+\frac{7}{8}\)
  12. \(4(2x-\frac{3}{5})=3x+\frac{4}{11}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{8}{11} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+154} & = & \color{red}{-264x} +24 \\\Leftrightarrow & -693x \color{red}{+154} \color{blue}{-154} \color{blue}{+264x} & = & \color{red}{-264x} +24 \color{blue}{+264x} \color{blue}{-154} \\\Leftrightarrow & -693x+264x& = & 24-154 \\\Leftrightarrow & \color{red}{-429} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{-429} & & \\\Leftrightarrow & x = \frac{10}{33} & & \\ & V = \left\{ \frac{10}{33} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{8})& = & -4x+\frac{4}{7} \\\Leftrightarrow & 9x-\frac{9}{8}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{504}{ \color{blue}{56} }x- \frac{63}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{-224x} +32 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{+224x} & = & \color{red}{-224x} +32 \color{blue}{+224x} \color{blue}{+63} \\\Leftrightarrow & 504x+224x& = & 32+63 \\\Leftrightarrow & \color{red}{728} x& = & 95 \\\Leftrightarrow & x = \frac{95}{728} & & \\ & V = \left\{ \frac{95}{728} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{385x} +40 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 660x-385x& = & 40-132 \\\Leftrightarrow & \color{red}{275} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{275} & & \\ & V = \left\{ \frac{-92}{275} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{6})& = & 6x+\frac{4}{5} \\\Leftrightarrow & -25x-\frac{25}{6}& = & 6x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-750}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{180}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -750x \color{red}{-125} & = & \color{red}{180x} +24 \\\Leftrightarrow & -750x \color{red}{-125} \color{blue}{+125} \color{blue}{-180x} & = & \color{red}{180x} +24 \color{blue}{-180x} \color{blue}{+125} \\\Leftrightarrow & -750x-180x& = & 24+125 \\\Leftrightarrow & \color{red}{-930} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-930} & & \\\Leftrightarrow & x = \frac{-149}{930} & & \\ & V = \left\{ \frac{-149}{930} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{315x} +40 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+28} \\\Leftrightarrow & 140x-315x& = & 40+28 \\\Leftrightarrow & \color{red}{-175} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-175} & & \\\Leftrightarrow & x = \frac{-68}{175} & & \\ & V = \left\{ \frac{-68}{175} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{+270} & = & \color{red}{495x} +110 \\\Leftrightarrow & 1782x \color{red}{+270} \color{blue}{-270} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{-270} \\\Leftrightarrow & 1782x-495x& = & 110-270 \\\Leftrightarrow & \color{red}{1287} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{1287} & & \\ & V = \left\{ \frac{-160}{1287} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{11})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -25x-\frac{25}{11}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3300}{ \color{blue}{132} }x- \frac{300}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3300x \color{red}{-300} & = & \color{red}{924x} +55 \\\Leftrightarrow & -3300x \color{red}{-300} \color{blue}{+300} \color{blue}{-924x} & = & \color{red}{924x} +55 \color{blue}{-924x} \color{blue}{+300} \\\Leftrightarrow & -3300x-924x& = & 55+300 \\\Leftrightarrow & \color{red}{-4224} x& = & 355 \\\Leftrightarrow & x = \frac{355}{-4224} & & \\\Leftrightarrow & x = \frac{-355}{4224} & & \\ & V = \left\{ \frac{-355}{4224} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+24} & = & \color{red}{45x} +4 \\\Leftrightarrow & 108x \color{red}{+24} \color{blue}{-24} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{-24} \\\Leftrightarrow & 108x-45x& = & 4-24 \\\Leftrightarrow & \color{red}{63} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{-231x} +12 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +12 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 660x+231x& = & 12+220 \\\Leftrightarrow & \color{red}{891} x& = & 232 \\\Leftrightarrow & x = \frac{232}{891} & & \\ & V = \left\{ \frac{232}{891} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & -2x+\frac{4}{3} \\\Leftrightarrow & -25x+\frac{10}{3}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{+10} & = & \color{red}{-6x} +4 \\\Leftrightarrow & -75x \color{red}{+10} \color{blue}{-10} \color{blue}{+6x} & = & \color{red}{-6x} +4 \color{blue}{+6x} \color{blue}{-10} \\\Leftrightarrow & -75x+6x& = & 4-10 \\\Leftrightarrow & \color{red}{-69} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-69} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{8}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x- \frac{64}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{-64} & = & \color{red}{392x} +49 \\\Leftrightarrow & -336x \color{red}{-64} \color{blue}{+64} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{+64} \\\Leftrightarrow & -336x-392x& = & 49+64 \\\Leftrightarrow & \color{red}{-728} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-728} & & \\\Leftrightarrow & x = \frac{-113}{728} & & \\ & V = \left\{ \frac{-113}{728} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{165x} +20 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +20 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & 440x-165x& = & 20+132 \\\Leftrightarrow & \color{red}{275} x& = & 152 \\\Leftrightarrow & x = \frac{152}{275} & & \\ & V = \left\{ \frac{152}{275} \right\} & \\\end{align}\)
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