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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-20} & = & \color{red}{135x} +54 \\\Leftrightarrow & 180x \color{red}{-20} \color{blue}{+20} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{+20} \\\Leftrightarrow & 180x-135x& = & 54+20 \\\Leftrightarrow & \color{red}{45} x& = & 74 \\\Leftrightarrow & x = \frac{74}{45} & & \\ & V = \left\{ \frac{74}{45} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+6} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -63x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -63x+35x& = & 2-6 \\\Leftrightarrow & \color{red}{-28} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-28} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-32} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 120x \color{red}{-32} \color{blue}{+32} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+32} \\\Leftrightarrow & 120x+54x& = & 27+32 \\\Leftrightarrow & \color{red}{174} x& = & 59 \\\Leftrightarrow & x = \frac{59}{174} & & \\ & V = \left\{ \frac{59}{174} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{5})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{5}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+88} & = & \color{red}{-495x} +30 \\\Leftrightarrow & 440x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +30 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & 440x+495x& = & 30-88 \\\Leftrightarrow & \color{red}{935} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{935} & & \\ & V = \left\{ \frac{-58}{935} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 8x-\frac{20}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{-40} & = & \color{red}{-42x} +15 \\\Leftrightarrow & 48x \color{red}{-40} \color{blue}{+40} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{+40} \\\Leftrightarrow & 48x+42x& = & 15+40 \\\Leftrightarrow & \color{red}{90} x& = & 55 \\\Leftrightarrow & x = \frac{55}{90} & & \\\Leftrightarrow & x = \frac{11}{18} & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{20}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-20} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 330x \color{red}{-20} \color{blue}{+20} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+20} \\\Leftrightarrow & 330x+385x& = & 66+20 \\\Leftrightarrow & \color{red}{715} x& = & 86 \\\Leftrightarrow & x = \frac{86}{715} & & \\ & V = \left\{ \frac{86}{715} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 8x+\frac{2}{11} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+154} & = & \color{red}{264x} +6 \\\Leftrightarrow & 1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-264x} & = & \color{red}{264x} +6 \color{blue}{-264x} \color{blue}{-154} \\\Leftrightarrow & 1155x-264x& = & 6-154 \\\Leftrightarrow & \color{red}{891} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{891} & & \\ & V = \left\{ \frac{-148}{891} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & -8x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{15}{8}& = & -8x+\frac{7}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{14}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{+45} & = & \color{red}{-192x} +14 \\\Leftrightarrow & -360x \color{red}{+45} \color{blue}{-45} \color{blue}{+192x} & = & \color{red}{-192x} +14 \color{blue}{+192x} \color{blue}{-45} \\\Leftrightarrow & -360x+192x& = & 14-45 \\\Leftrightarrow & \color{red}{-168} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-168} & & \\\Leftrightarrow & x = \frac{31}{168} & & \\ & V = \left\{ \frac{31}{168} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{15}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-105} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -924x \color{red}{-105} \color{blue}{+105} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+105} \\\Leftrightarrow & -924x+385x& = & 44+105 \\\Leftrightarrow & \color{red}{-539} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-539} & & \\\Leftrightarrow & x = \frac{-149}{539} & & \\ & V = \left\{ \frac{-149}{539} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-162} & = & \color{red}{495x} +110 \\\Leftrightarrow & -1188x \color{red}{-162} \color{blue}{+162} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+162} \\\Leftrightarrow & -1188x-495x& = & 110+162 \\\Leftrightarrow & \color{red}{-1683} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-1683} & & \\\Leftrightarrow & x = \frac{-16}{99} & & \\ & V = \left\{ \frac{-16}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{3})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-220} & = & \color{red}{-297x} +24 \\\Leftrightarrow & -660x \color{red}{-220} \color{blue}{+220} \color{blue}{+297x} & = & \color{red}{-297x} +24 \color{blue}{+297x} \color{blue}{+220} \\\Leftrightarrow & -660x+297x& = & 24+220 \\\Leftrightarrow & \color{red}{-363} x& = & 244 \\\Leftrightarrow & x = \frac{244}{-363} & & \\\Leftrightarrow & x = \frac{-244}{363} & & \\ & V = \left\{ \frac{-244}{363} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+9} & = & \color{red}{-50x} +6 \\\Leftrightarrow & -120x \color{red}{+9} \color{blue}{-9} \color{blue}{+50x} & = & \color{red}{-50x} +6 \color{blue}{+50x} \color{blue}{-9} \\\Leftrightarrow & -120x+50x& = & 6-9 \\\Leftrightarrow & \color{red}{-70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-70} & & \\\Leftrightarrow & x = \frac{3}{70} & & \\ & V = \left\{ \frac{3}{70} \right\} & \\\end{align}\)
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