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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{15}{4}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{+165} & = & \color{red}{-308x} +24 \\\Leftrightarrow & -880x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +24 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -880x+308x& = & 24-165 \\\Leftrightarrow & \color{red}{-572} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-572} & & \\\Leftrightarrow & x = \frac{141}{572} & & \\ & V = \left\{ \frac{141}{572} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{28}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{18x} +27 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{+56} \\\Leftrightarrow & 84x-18x& = & 27+56 \\\Leftrightarrow & \color{red}{66} x& = & 83 \\\Leftrightarrow & x = \frac{83}{66} & & \\ & V = \left\{ \frac{83}{66} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{7})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{9}{7}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{27}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-27} & = & \color{red}{-42x} +14 \\\Leftrightarrow & 315x \color{red}{-27} \color{blue}{+27} \color{blue}{+42x} & = & \color{red}{-42x} +14 \color{blue}{+42x} \color{blue}{+27} \\\Leftrightarrow & 315x+42x& = & 14+27 \\\Leftrightarrow & \color{red}{357} x& = & 41 \\\Leftrightarrow & x = \frac{41}{357} & & \\ & V = \left\{ \frac{41}{357} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{12}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{24}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-24} & = & \color{red}{98x} +21 \\\Leftrightarrow & 112x \color{red}{-24} \color{blue}{+24} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+24} \\\Leftrightarrow & 112x-98x& = & 21+24 \\\Leftrightarrow & \color{red}{14} x& = & 45 \\\Leftrightarrow & x = \frac{45}{14} & & \\ & V = \left\{ \frac{45}{14} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 4x+\frac{7}{8} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-80} & = & \color{red}{224x} +49 \\\Leftrightarrow & -840x \color{red}{-80} \color{blue}{+80} \color{blue}{-224x} & = & \color{red}{224x} +49 \color{blue}{-224x} \color{blue}{+80} \\\Leftrightarrow & -840x-224x& = & 49+80 \\\Leftrightarrow & \color{red}{-1064} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-1064} & & \\\Leftrightarrow & x = \frac{-129}{1064} & & \\ & V = \left\{ \frac{-129}{1064} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{10}{7}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{-50} & = & \color{red}{-280x} +42 \\\Leftrightarrow & 875x \color{red}{-50} \color{blue}{+50} \color{blue}{+280x} & = & \color{red}{-280x} +42 \color{blue}{+280x} \color{blue}{+50} \\\Leftrightarrow & 875x+280x& = & 42+50 \\\Leftrightarrow & \color{red}{1155} x& = & 92 \\\Leftrightarrow & x = \frac{92}{1155} & & \\ & V = \left\{ \frac{92}{1155} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{9})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -25x+\frac{20}{9}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+140} & = & \color{red}{-189x} +27 \\\Leftrightarrow & -1575x \color{red}{+140} \color{blue}{-140} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{-140} \\\Leftrightarrow & -1575x+189x& = & 27-140 \\\Leftrightarrow & \color{red}{-1386} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-1386} & & \\\Leftrightarrow & x = \frac{113}{1386} & & \\ & V = \left\{ \frac{113}{1386} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{20}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-140} & = & \color{red}{441x} +90 \\\Leftrightarrow & -1008x \color{red}{-140} \color{blue}{+140} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+140} \\\Leftrightarrow & -1008x-441x& = & 90+140 \\\Leftrightarrow & \color{red}{-1449} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1449} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{8})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -25x+\frac{15}{8}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1000}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1000x \color{red}{+75} & = & \color{red}{-360x} +64 \\\Leftrightarrow & -1000x \color{red}{+75} \color{blue}{-75} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{-75} \\\Leftrightarrow & -1000x+360x& = & 64-75 \\\Leftrightarrow & \color{red}{-640} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-640} & & \\\Leftrightarrow & x = \frac{11}{640} & & \\ & V = \left\{ \frac{11}{640} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{4})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{9}{4}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x- \frac{45}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{-45} & = & \color{red}{100x} +6 \\\Leftrightarrow & 120x \color{red}{-45} \color{blue}{+45} \color{blue}{-100x} & = & \color{red}{100x} +6 \color{blue}{-100x} \color{blue}{+45} \\\Leftrightarrow & 120x-100x& = & 6+45 \\\Leftrightarrow & \color{red}{20} x& = & 51 \\\Leftrightarrow & x = \frac{51}{20} & & \\ & V = \left\{ \frac{51}{20} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{-15} & = & \color{red}{-56x} +36 \\\Leftrightarrow & 96x \color{red}{-15} \color{blue}{+15} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{+15} \\\Leftrightarrow & 96x+56x& = & 36+15 \\\Leftrightarrow & \color{red}{152} x& = & 51 \\\Leftrightarrow & x = \frac{51}{152} & & \\ & V = \left\{ \frac{51}{152} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{7})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-160} & = & \color{red}{-504x} +35 \\\Leftrightarrow & 1120x \color{red}{-160} \color{blue}{+160} \color{blue}{+504x} & = & \color{red}{-504x} +35 \color{blue}{+504x} \color{blue}{+160} \\\Leftrightarrow & 1120x+504x& = & 35+160 \\\Leftrightarrow & \color{red}{1624} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1624} & & \\ & V = \left\{ \frac{195}{1624} \right\} & \\\end{align}\)
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