Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-196x} +63 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+196x} & = & \color{red}{-196x} +63 \color{blue}{+196x} \color{blue}{+40} \\\Leftrightarrow & -280x+196x& = & 63+40 \\\Leftrightarrow & \color{red}{-84} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-84} & & \\\Leftrightarrow & x = \frac{-103}{84} & & \\ & V = \left\{ \frac{-103}{84} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{7})& = & 9x+\frac{7}{4} \\\Leftrightarrow & -8x+\frac{8}{7}& = & 9x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{+32} & = & \color{red}{252x} +49 \\\Leftrightarrow & -224x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +49 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -224x-252x& = & 49-32 \\\Leftrightarrow & \color{red}{-476} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-476} & & \\\Leftrightarrow & x = \frac{-1}{28} & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{11})& = & -3x+\frac{7}{9} \\\Leftrightarrow & -25x-\frac{10}{11}& = & -3x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{-90} & = & \color{red}{-297x} +77 \\\Leftrightarrow & -2475x \color{red}{-90} \color{blue}{+90} \color{blue}{+297x} & = & \color{red}{-297x} +77 \color{blue}{+297x} \color{blue}{+90} \\\Leftrightarrow & -2475x+297x& = & 77+90 \\\Leftrightarrow & \color{red}{-2178} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-2178} & & \\\Leftrightarrow & x = \frac{-167}{2178} & & \\ & V = \left\{ \frac{-167}{2178} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{5})& = & 3x+\frac{9}{11} \\\Leftrightarrow & 28x-\frac{14}{5}& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-154} & = & \color{red}{165x} +45 \\\Leftrightarrow & 1540x \color{red}{-154} \color{blue}{+154} \color{blue}{-165x} & = & \color{red}{165x} +45 \color{blue}{-165x} \color{blue}{+154} \\\Leftrightarrow & 1540x-165x& = & 45+154 \\\Leftrightarrow & \color{red}{1375} x& = & 199 \\\Leftrightarrow & x = \frac{199}{1375} & & \\ & V = \left\{ \frac{199}{1375} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{9})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 8x-\frac{4}{9}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-44} & = & \color{red}{-495x} +18 \\\Leftrightarrow & 792x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +18 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & 792x+495x& = & 18+44 \\\Leftrightarrow & \color{red}{1287} x& = & 62 \\\Leftrightarrow & x = \frac{62}{1287} & & \\ & V = \left\{ \frac{62}{1287} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{2})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{25}{2}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+225} & = & \color{red}{-54x} +16 \\\Leftrightarrow & 180x \color{red}{+225} \color{blue}{-225} \color{blue}{+54x} & = & \color{red}{-54x} +16 \color{blue}{+54x} \color{blue}{-225} \\\Leftrightarrow & 180x+54x& = & 16-225 \\\Leftrightarrow & \color{red}{234} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{234} & & \\ & V = \left\{ \frac{-209}{234} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +15 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 15-132 \\\Leftrightarrow & \color{red}{-935} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-935} & & \\\Leftrightarrow & x = \frac{117}{935} & & \\ & V = \left\{ \frac{117}{935} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{-108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -1080x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & -1080x+225x& = & 10+108 \\\Leftrightarrow & \color{red}{-855} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-855} & & \\\Leftrightarrow & x = \frac{-118}{855} & & \\ & V = \left\{ \frac{-118}{855} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & 4x+\frac{2}{9} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{-270} & = & \color{red}{252x} +14 \\\Leftrightarrow & -1134x \color{red}{-270} \color{blue}{+270} \color{blue}{-252x} & = & \color{red}{252x} +14 \color{blue}{-252x} \color{blue}{+270} \\\Leftrightarrow & -1134x-252x& = & 14+270 \\\Leftrightarrow & \color{red}{-1386} x& = & 284 \\\Leftrightarrow & x = \frac{284}{-1386} & & \\\Leftrightarrow & x = \frac{-142}{693} & & \\ & V = \left\{ \frac{-142}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{8})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{15}{8}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -80x+56x& = & 6-15 \\\Leftrightarrow & \color{red}{-24} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-24} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{3})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{-105x} +24 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -150x+105x& = & 24-50 \\\Leftrightarrow & \color{red}{-45} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-45} & & \\\Leftrightarrow & x = \frac{26}{45} & & \\ & V = \left\{ \frac{26}{45} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2640}{ \color{blue}{110} }x- \frac{240}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2640x \color{red}{-240} & = & \color{red}{770x} +99 \\\Leftrightarrow & 2640x \color{red}{-240} \color{blue}{+240} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{+240} \\\Leftrightarrow & 2640x-770x& = & 99+240 \\\Leftrightarrow & \color{red}{1870} x& = & 339 \\\Leftrightarrow & x = \frac{339}{1870} & & \\ & V = \left\{ \frac{339}{1870} \right\} & \\\end{align}\)
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