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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{16}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{165x} +110 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-48} \\\Leftrightarrow & 396x-165x& = & 110-48 \\\Leftrightarrow & \color{red}{231} x& = & 62 \\\Leftrightarrow & x = \frac{62}{231} & & \\ & V = \left\{ \frac{62}{231} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{8})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{+21} & = & \color{red}{40x} +6 \\\Leftrightarrow & -112x \color{red}{+21} \color{blue}{-21} \color{blue}{-40x} & = & \color{red}{40x} +6 \color{blue}{-40x} \color{blue}{-21} \\\Leftrightarrow & -112x-40x& = & 6-21 \\\Leftrightarrow & \color{red}{-152} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-152} & & \\\Leftrightarrow & x = \frac{15}{152} & & \\ & V = \left\{ \frac{15}{152} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{11})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -10x+\frac{8}{11}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{+64} & = & \color{red}{616x} +33 \\\Leftrightarrow & -880x \color{red}{+64} \color{blue}{-64} \color{blue}{-616x} & = & \color{red}{616x} +33 \color{blue}{-616x} \color{blue}{-64} \\\Leftrightarrow & -880x-616x& = & 33-64 \\\Leftrightarrow & \color{red}{-1496} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1496} & & \\\Leftrightarrow & x = \frac{31}{1496} & & \\ & V = \left\{ \frac{31}{1496} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+175} & = & \color{red}{98x} +8 \\\Leftrightarrow & -140x \color{red}{+175} \color{blue}{-175} \color{blue}{-98x} & = & \color{red}{98x} +8 \color{blue}{-98x} \color{blue}{-175} \\\Leftrightarrow & -140x-98x& = & 8-175 \\\Leftrightarrow & \color{red}{-238} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-238} & & \\\Leftrightarrow & x = \frac{167}{238} & & \\ & V = \left\{ \frac{167}{238} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{220x} +22 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{-220x} & = & \color{red}{220x} +22 \color{blue}{-220x} \color{blue}{-90} \\\Leftrightarrow & -990x-220x& = & 22-90 \\\Leftrightarrow & \color{red}{-1210} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1210} & & \\\Leftrightarrow & x = \frac{34}{605} & & \\ & V = \left\{ \frac{34}{605} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{2})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 28x+\frac{21}{2}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x+ \frac{105}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{+105} & = & \color{red}{50x} +4 \\\Leftrightarrow & 280x \color{red}{+105} \color{blue}{-105} \color{blue}{-50x} & = & \color{red}{50x} +4 \color{blue}{-50x} \color{blue}{-105} \\\Leftrightarrow & 280x-50x& = & 4-105 \\\Leftrightarrow & \color{red}{230} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{230} & & \\ & V = \left\{ \frac{-101}{230} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{2})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{25}{2}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-75} & = & \color{red}{-54x} +4 \\\Leftrightarrow & 120x \color{red}{-75} \color{blue}{+75} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{+75} \\\Leftrightarrow & 120x+54x& = & 4+75 \\\Leftrightarrow & \color{red}{174} x& = & 79 \\\Leftrightarrow & x = \frac{79}{174} & & \\ & V = \left\{ \frac{79}{174} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+14} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -84x \color{red}{+14} \color{blue}{-14} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-14} \\\Leftrightarrow & -84x+21x& = & 10-14 \\\Leftrightarrow & \color{red}{-63} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-63} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{275x} +50 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 990x-275x& = & 50-132 \\\Leftrightarrow & \color{red}{715} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{715} & & \\ & V = \left\{ \frac{-82}{715} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-176} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 1232x \color{red}{-176} \color{blue}{+176} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+176} \\\Leftrightarrow & 1232x+385x& = & 14+176 \\\Leftrightarrow & \color{red}{1617} x& = & 190 \\\Leftrightarrow & x = \frac{190}{1617} & & \\ & V = \left\{ \frac{190}{1617} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{9}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{9}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{80x} +72 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{-80x} & = & \color{red}{80x} +72 \color{blue}{-80x} \color{blue}{+105} \\\Leftrightarrow & 840x-80x& = & 72+105 \\\Leftrightarrow & \color{red}{760} x& = & 177 \\\Leftrightarrow & x = \frac{177}{760} & & \\ & V = \left\{ \frac{177}{760} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{9})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 4x+\frac{10}{9}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{72}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 72x \color{red}{+20} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 72x \color{red}{+20} \color{blue}{-20} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-20} \\\Leftrightarrow & 72x+54x& = & 27-20 \\\Leftrightarrow & \color{red}{126} x& = & 7 \\\Leftrightarrow & x = \frac{7}{126} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
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