Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-80} & = & \color{red}{105x} +28 \\\Leftrightarrow & -700x \color{red}{-80} \color{blue}{+80} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+80} \\\Leftrightarrow & -700x-105x& = & 28+80 \\\Leftrightarrow & \color{red}{-805} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-805} & & \\\Leftrightarrow & x = \frac{-108}{805} & & \\ & V = \left\{ \frac{-108}{805} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{4})& = & -4x+\frac{2}{7} \\\Leftrightarrow & -15x+\frac{25}{4}& = & -4x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{-112x} +8 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{+112x} & = & \color{red}{-112x} +8 \color{blue}{+112x} \color{blue}{-175} \\\Leftrightarrow & -420x+112x& = & 8-175 \\\Leftrightarrow & \color{red}{-308} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-308} & & \\\Leftrightarrow & x = \frac{167}{308} & & \\ & V = \left\{ \frac{167}{308} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{-12} & = & \color{red}{-15x} +6 \\\Leftrightarrow & 80x \color{red}{-12} \color{blue}{+12} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{+12} \\\Leftrightarrow & 80x+15x& = & 6+12 \\\Leftrightarrow & \color{red}{95} x& = & 18 \\\Leftrightarrow & x = \frac{18}{95} & & \\ & V = \left\{ \frac{18}{95} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-308} & = & \color{red}{-264x} +18 \\\Leftrightarrow & -693x \color{red}{-308} \color{blue}{+308} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{+308} \\\Leftrightarrow & -693x+264x& = & 18+308 \\\Leftrightarrow & \color{red}{-429} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-429} & & \\\Leftrightarrow & x = \frac{-326}{429} & & \\ & V = \left\{ \frac{-326}{429} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{11})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 6x-\frac{10}{11}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{792}{ \color{blue}{132} }x- \frac{120}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 792x \color{red}{-120} & = & \color{red}{-660x} +77 \\\Leftrightarrow & 792x \color{red}{-120} \color{blue}{+120} \color{blue}{+660x} & = & \color{red}{-660x} +77 \color{blue}{+660x} \color{blue}{+120} \\\Leftrightarrow & 792x+660x& = & 77+120 \\\Leftrightarrow & \color{red}{1452} x& = & 197 \\\Leftrightarrow & x = \frac{197}{1452} & & \\ & V = \left\{ \frac{197}{1452} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{10}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+50} & = & \color{red}{-405x} +54 \\\Leftrightarrow & 360x \color{red}{+50} \color{blue}{-50} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{-50} \\\Leftrightarrow & 360x+405x& = & 54-50 \\\Leftrightarrow & \color{red}{765} x& = & 4 \\\Leftrightarrow & x = \frac{4}{765} & & \\ & V = \left\{ \frac{4}{765} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{2})& = & -6x+\frac{3}{10} \\\Leftrightarrow & -28x-\frac{21}{2}& = & -6x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{-60}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{-60x} +3 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{+60x} & = & \color{red}{-60x} +3 \color{blue}{+60x} \color{blue}{+105} \\\Leftrightarrow & -280x+60x& = & 3+105 \\\Leftrightarrow & \color{red}{-220} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-220} & & \\\Leftrightarrow & x = \frac{-27}{55} & & \\ & V = \left\{ \frac{-27}{55} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{2})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{9}{2}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x- \frac{27}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{-27} & = & \color{red}{42x} +8 \\\Leftrightarrow & 36x \color{red}{-27} \color{blue}{+27} \color{blue}{-42x} & = & \color{red}{42x} +8 \color{blue}{-42x} \color{blue}{+27} \\\Leftrightarrow & 36x-42x& = & 8+27 \\\Leftrightarrow & \color{red}{-6} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-6} & & \\\Leftrightarrow & x = \frac{-35}{6} & & \\ & V = \left\{ \frac{-35}{6} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{105x} +50 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 450x-105x& = & 50-72 \\\Leftrightarrow & \color{red}{345} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{345} & & \\ & V = \left\{ \frac{-22}{345} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+20} & = & \color{red}{42x} +27 \\\Leftrightarrow & 48x \color{red}{+20} \color{blue}{-20} \color{blue}{-42x} & = & \color{red}{42x} +27 \color{blue}{-42x} \color{blue}{-20} \\\Leftrightarrow & 48x-42x& = & 27-20 \\\Leftrightarrow & \color{red}{6} x& = & 7 \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{9})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{14}{9}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+14} & = & \color{red}{-45x} +24 \\\Leftrightarrow & 189x \color{red}{+14} \color{blue}{-14} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{-14} \\\Leftrightarrow & 189x+45x& = & 24-14 \\\Leftrightarrow & \color{red}{234} x& = & 10 \\\Leftrightarrow & x = \frac{10}{234} & & \\\Leftrightarrow & x = \frac{5}{117} & & \\ & V = \left\{ \frac{5}{117} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{75x} +25 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +25 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 240x-75x& = & 25-36 \\\Leftrightarrow & \color{red}{165} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{165} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
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