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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x-\frac{6}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{24}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-140x} +15 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+24} \\\Leftrightarrow & -120x+140x& = & 15+24 \\\Leftrightarrow & \color{red}{20} x& = & 39 \\\Leftrightarrow & x = \frac{39}{20} & & \\ & V = \left\{ \frac{39}{20} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{12}{11}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{-24} & = & \color{red}{198x} +55 \\\Leftrightarrow & -176x \color{red}{-24} \color{blue}{+24} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{+24} \\\Leftrightarrow & -176x-198x& = & 55+24 \\\Leftrightarrow & \color{red}{-374} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-374} & & \\\Leftrightarrow & x = \frac{-79}{374} & & \\ & V = \left\{ \frac{-79}{374} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{7})& = & 8x+\frac{9}{7} \\\Leftrightarrow & -25x+\frac{25}{7}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+25} & = & \color{red}{56x} +9 \\\Leftrightarrow & -175x \color{red}{+25} \color{blue}{-25} \color{blue}{-56x} & = & \color{red}{56x} +9 \color{blue}{-56x} \color{blue}{-25} \\\Leftrightarrow & -175x-56x& = & 9-25 \\\Leftrightarrow & \color{red}{-231} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-231} & & \\\Leftrightarrow & x = \frac{16}{231} & & \\ & V = \left\{ \frac{16}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{+4} & = & \color{red}{45x} +8 \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-4} \\\Leftrightarrow & -20x-45x& = & 8-4 \\\Leftrightarrow & \color{red}{-65} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-65} & & \\\Leftrightarrow & x = \frac{-4}{65} & & \\ & V = \left\{ \frac{-4}{65} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 880x+385x& = & 30-132 \\\Leftrightarrow & \color{red}{1265} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{1265} & & \\ & V = \left\{ \frac{-102}{1265} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+45} & = & \color{red}{-84x} +40 \\\Leftrightarrow & 300x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +40 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & 300x+84x& = & 40-45 \\\Leftrightarrow & \color{red}{384} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{384} & & \\ & V = \left\{ \frac{-5}{384} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{9})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{4}{9}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+4} & = & \color{red}{-45x} +4 \\\Leftrightarrow & 54x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & 54x+45x& = & 4-4 \\\Leftrightarrow & \color{red}{99} x& = & 0 \\\Leftrightarrow & x = \frac{0}{99} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & -8x+\frac{16}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+176} & = & \color{red}{297x} +12 \\\Leftrightarrow & -264x \color{red}{+176} \color{blue}{-176} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{-176} \\\Leftrightarrow & -264x-297x& = & 12-176 \\\Leftrightarrow & \color{red}{-561} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{-561} & & \\\Leftrightarrow & x = \frac{164}{561} & & \\ & V = \left\{ \frac{164}{561} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{15}{2}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{50x} +8 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{-50x} & = & \color{red}{50x} +8 \color{blue}{-50x} \color{blue}{-75} \\\Leftrightarrow & -120x-50x& = & 8-75 \\\Leftrightarrow & \color{red}{-170} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-170} & & \\\Leftrightarrow & x = \frac{67}{170} & & \\ & V = \left\{ \frac{67}{170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{165x} +88 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -792x-165x& = & 88+54 \\\Leftrightarrow & \color{red}{-957} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-957} & & \\\Leftrightarrow & x = \frac{-142}{957} & & \\ & V = \left\{ \frac{-142}{957} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & 3x+\frac{7}{9} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{105}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{54x} +14 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{-54x} & = & \color{red}{54x} +14 \color{blue}{-54x} \color{blue}{+105} \\\Leftrightarrow & 252x-54x& = & 14+105 \\\Leftrightarrow & \color{red}{198} x& = & 119 \\\Leftrightarrow & x = \frac{119}{198} & & \\ & V = \left\{ \frac{119}{198} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{-308x} +20 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{+308x} & = & \color{red}{-308x} +20 \color{blue}{+308x} \color{blue}{+165} \\\Leftrightarrow & -880x+308x& = & 20+165 \\\Leftrightarrow & \color{red}{-572} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-572} & & \\\Leftrightarrow & x = \frac{-185}{572} & & \\ & V = \left\{ \frac{-185}{572} \right\} & \\\end{align}\)
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