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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-216} & = & \color{red}{315x} +20 \\\Leftrightarrow & 1350x \color{red}{-216} \color{blue}{+216} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{+216} \\\Leftrightarrow & 1350x-315x& = & 20+216 \\\Leftrightarrow & \color{red}{1035} x& = & 236 \\\Leftrightarrow & x = \frac{236}{1035} & & \\ & V = \left\{ \frac{236}{1035} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{3})& = & -2x+\frac{7}{4} \\\Leftrightarrow & 21x-\frac{28}{3}& = & -2x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-112} & = & \color{red}{-24x} +21 \\\Leftrightarrow & 252x \color{red}{-112} \color{blue}{+112} \color{blue}{+24x} & = & \color{red}{-24x} +21 \color{blue}{+24x} \color{blue}{+112} \\\Leftrightarrow & 252x+24x& = & 21+112 \\\Leftrightarrow & \color{red}{276} x& = & 133 \\\Leftrightarrow & x = \frac{133}{276} & & \\ & V = \left\{ \frac{133}{276} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{2})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{25}{2}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-75} & = & \color{red}{42x} +16 \\\Leftrightarrow & -60x \color{red}{-75} \color{blue}{+75} \color{blue}{-42x} & = & \color{red}{42x} +16 \color{blue}{-42x} \color{blue}{+75} \\\Leftrightarrow & -60x-42x& = & 16+75 \\\Leftrightarrow & \color{red}{-102} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-102} & & \\\Leftrightarrow & x = \frac{-91}{102} & & \\ & V = \left\{ \frac{-91}{102} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{105x} +14 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 140x-105x& = & 14+30 \\\Leftrightarrow & \color{red}{35} x& = & 44 \\\Leftrightarrow & x = \frac{44}{35} & & \\ & V = \left\{ \frac{44}{35} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{11})& = & 6x+\frac{10}{11} \\\Leftrightarrow & 35x+\frac{21}{11}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+21} & = & \color{red}{66x} +10 \\\Leftrightarrow & 385x \color{red}{+21} \color{blue}{-21} \color{blue}{-66x} & = & \color{red}{66x} +10 \color{blue}{-66x} \color{blue}{-21} \\\Leftrightarrow & 385x-66x& = & 10-21 \\\Leftrightarrow & \color{red}{319} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{319} & & \\\Leftrightarrow & x = \frac{-1}{29} & & \\ & V = \left\{ \frac{-1}{29} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{25x} +6 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 90x-25x& = & 6+24 \\\Leftrightarrow & \color{red}{65} x& = & 30 \\\Leftrightarrow & x = \frac{30}{65} & & \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{12}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-36} & = & \color{red}{231x} +22 \\\Leftrightarrow & 198x \color{red}{-36} \color{blue}{+36} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+36} \\\Leftrightarrow & 198x-231x& = & 22+36 \\\Leftrightarrow & \color{red}{-33} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-33} & & \\\Leftrightarrow & x = \frac{-58}{33} & & \\ & V = \left\{ \frac{-58}{33} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{4})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -9x-\frac{9}{4}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{45}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{100x} +6 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{-100x} & = & \color{red}{100x} +6 \color{blue}{-100x} \color{blue}{+45} \\\Leftrightarrow & -180x-100x& = & 6+45 \\\Leftrightarrow & \color{red}{-280} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-280} & & \\\Leftrightarrow & x = \frac{-51}{280} & & \\ & V = \left\{ \frac{-51}{280} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & 4x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{+15} & = & \color{red}{16x} +3 \\\Leftrightarrow & -60x \color{red}{+15} \color{blue}{-15} \color{blue}{-16x} & = & \color{red}{16x} +3 \color{blue}{-16x} \color{blue}{-15} \\\Leftrightarrow & -60x-16x& = & 3-15 \\\Leftrightarrow & \color{red}{-76} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-76} & & \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-480}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -480x \color{red}{+96} & = & \color{red}{100x} +45 \\\Leftrightarrow & -480x \color{red}{+96} \color{blue}{-96} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{-96} \\\Leftrightarrow & -480x-100x& = & 45-96 \\\Leftrightarrow & \color{red}{-580} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-580} & & \\\Leftrightarrow & x = \frac{51}{580} & & \\ & V = \left\{ \frac{51}{580} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{4})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{25}{4}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+125} & = & \color{red}{140x} +6 \\\Leftrightarrow & -400x \color{red}{+125} \color{blue}{-125} \color{blue}{-140x} & = & \color{red}{140x} +6 \color{blue}{-140x} \color{blue}{-125} \\\Leftrightarrow & -400x-140x& = & 6-125 \\\Leftrightarrow & \color{red}{-540} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-540} & & \\\Leftrightarrow & x = \frac{119}{540} & & \\ & V = \left\{ \frac{119}{540} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{140x} +8 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{-140x} & = & \color{red}{140x} +8 \color{blue}{-140x} \color{blue}{-75} \\\Leftrightarrow & -120x-140x& = & 8-75 \\\Leftrightarrow & \color{red}{-260} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-260} & & \\\Leftrightarrow & x = \frac{67}{260} & & \\ & V = \left\{ \frac{67}{260} \right\} & \\\end{align}\)
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