Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{3})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{105x} +24 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -150x-105x& = & 24-50 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -8x-\frac{6}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-66} & = & \color{red}{-165x} +25 \\\Leftrightarrow & -440x \color{red}{-66} \color{blue}{+66} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{+66} \\\Leftrightarrow & -440x+165x& = & 25+66 \\\Leftrightarrow & \color{red}{-275} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-275} & & \\\Leftrightarrow & x = \frac{-91}{275} & & \\ & V = \left\{ \frac{-91}{275} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{1}{2})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{5}{2}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} })& = & (\frac{-8}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{+5} & = & \color{red}{-8x} +3 \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{+8x} & = & \color{red}{-8x} +3 \color{blue}{+8x} \color{blue}{-5} \\\Leftrightarrow & -30x+8x& = & 3-5 \\\Leftrightarrow & \color{red}{-22} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-22} & & \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1980}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1980x \color{red}{-108} & = & \color{red}{-462x} +55 \\\Leftrightarrow & 1980x \color{red}{-108} \color{blue}{+108} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+108} \\\Leftrightarrow & 1980x+462x& = & 55+108 \\\Leftrightarrow & \color{red}{2442} x& = & 163 \\\Leftrightarrow & x = \frac{163}{2442} & & \\ & V = \left\{ \frac{163}{2442} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+75} & = & \color{red}{100x} +8 \\\Leftrightarrow & -240x \color{red}{+75} \color{blue}{-75} \color{blue}{-100x} & = & \color{red}{100x} +8 \color{blue}{-100x} \color{blue}{-75} \\\Leftrightarrow & -240x-100x& = & 8-75 \\\Leftrightarrow & \color{red}{-340} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-340} & & \\\Leftrightarrow & x = \frac{67}{340} & & \\ & V = \left\{ \frac{67}{340} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{7})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{150}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+150} & = & \color{red}{-490x} +21 \\\Leftrightarrow & 1050x \color{red}{+150} \color{blue}{-150} \color{blue}{+490x} & = & \color{red}{-490x} +21 \color{blue}{+490x} \color{blue}{-150} \\\Leftrightarrow & 1050x+490x& = & 21-150 \\\Leftrightarrow & \color{red}{1540} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{1540} & & \\ & V = \left\{ \frac{-129}{1540} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 8x-\frac{4}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{8}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-8} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 112x \color{red}{-8} \color{blue}{+8} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+8} \\\Leftrightarrow & 112x+98x& = & 49+8 \\\Leftrightarrow & \color{red}{210} x& = & 57 \\\Leftrightarrow & x = \frac{57}{210} & & \\\Leftrightarrow & x = \frac{19}{70} & & \\ & V = \left\{ \frac{19}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{50x} +9 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -120x-50x& = & 9+24 \\\Leftrightarrow & \color{red}{-170} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-170} & & \\\Leftrightarrow & x = \frac{-33}{170} & & \\ & V = \left\{ \frac{-33}{170} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{10}{3}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+30} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 72x \color{red}{+30} \color{blue}{-30} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{-30} \\\Leftrightarrow & 72x+81x& = & 10-30 \\\Leftrightarrow & \color{red}{153} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{153} & & \\ & V = \left\{ \frac{-20}{153} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{10}{3}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+40} & = & \color{red}{96x} +9 \\\Leftrightarrow & -180x \color{red}{+40} \color{blue}{-40} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{-40} \\\Leftrightarrow & -180x-96x& = & 9-40 \\\Leftrightarrow & \color{red}{-276} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-276} & & \\\Leftrightarrow & x = \frac{31}{276} & & \\ & V = \left\{ \frac{31}{276} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{8})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{35}{8}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{320x} +64 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{-320x} & = & \color{red}{320x} +64 \color{blue}{-320x} \color{blue}{+175} \\\Leftrightarrow & -840x-320x& = & 64+175 \\\Leftrightarrow & \color{red}{-1160} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-1160} & & \\\Leftrightarrow & x = \frac{-239}{1160} & & \\ & V = \left\{ \frac{-239}{1160} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{105x} +27 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & 240x-105x& = & 27-100 \\\Leftrightarrow & \color{red}{135} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{135} & & \\ & V = \left\{ \frac{-73}{135} \right\} & \\\end{align}\)
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