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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{9})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{720}{ \color{blue}{90} }x- \frac{40}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 720x \color{red}{-40} & = & \color{red}{270x} +27 \\\Leftrightarrow & 720x \color{red}{-40} \color{blue}{+40} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+40} \\\Leftrightarrow & 720x-270x& = & 27+40 \\\Leftrightarrow & \color{red}{450} x& = & 67 \\\Leftrightarrow & x = \frac{67}{450} & & \\ & V = \left\{ \frac{67}{450} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -210x+49x& = & 3-30 \\\Leftrightarrow & \color{red}{-161} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-161} & & \\\Leftrightarrow & x = \frac{27}{161} & & \\ & V = \left\{ \frac{27}{161} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{7})& = & -6x+\frac{2}{9} \\\Leftrightarrow & 25x+\frac{15}{7}& = & -6x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{-378}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{+135} & = & \color{red}{-378x} +14 \\\Leftrightarrow & 1575x \color{red}{+135} \color{blue}{-135} \color{blue}{+378x} & = & \color{red}{-378x} +14 \color{blue}{+378x} \color{blue}{-135} \\\Leftrightarrow & 1575x+378x& = & 14-135 \\\Leftrightarrow & \color{red}{1953} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{1953} & & \\ & V = \left\{ \frac{-121}{1953} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & 3x+\frac{5}{6} \\\Leftrightarrow & 8x-\frac{6}{7}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{336}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 336x \color{red}{-36} & = & \color{red}{126x} +35 \\\Leftrightarrow & 336x \color{red}{-36} \color{blue}{+36} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{+36} \\\Leftrightarrow & 336x-126x& = & 35+36 \\\Leftrightarrow & \color{red}{210} x& = & 71 \\\Leftrightarrow & x = \frac{71}{210} & & \\ & V = \left\{ \frac{71}{210} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{9})& = & 8x+\frac{8}{7} \\\Leftrightarrow & -15x-\frac{20}{9}& = & 8x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-140} & = & \color{red}{504x} +72 \\\Leftrightarrow & -945x \color{red}{-140} \color{blue}{+140} \color{blue}{-504x} & = & \color{red}{504x} +72 \color{blue}{-504x} \color{blue}{+140} \\\Leftrightarrow & -945x-504x& = & 72+140 \\\Leftrightarrow & \color{red}{-1449} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-1449} & & \\\Leftrightarrow & x = \frac{-212}{1449} & & \\ & V = \left\{ \frac{-212}{1449} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{12})& = & 8x+\frac{5}{3} \\\Leftrightarrow & -15x+\frac{25}{12}& = & 8x+\frac{5}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{20}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+25} & = & \color{red}{96x} +20 \\\Leftrightarrow & -180x \color{red}{+25} \color{blue}{-25} \color{blue}{-96x} & = & \color{red}{96x} +20 \color{blue}{-96x} \color{blue}{-25} \\\Leftrightarrow & -180x-96x& = & 20-25 \\\Leftrightarrow & \color{red}{-276} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-276} & & \\\Leftrightarrow & x = \frac{5}{276} & & \\ & V = \left\{ \frac{5}{276} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{6}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+12} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -100x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & -100x+70x& = & 3-12 \\\Leftrightarrow & \color{red}{-30} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-30} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{20}{11}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+20} & = & \color{red}{-33x} +4 \\\Leftrightarrow & 110x \color{red}{+20} \color{blue}{-20} \color{blue}{+33x} & = & \color{red}{-33x} +4 \color{blue}{+33x} \color{blue}{-20} \\\Leftrightarrow & 110x+33x& = & 4-20 \\\Leftrightarrow & \color{red}{143} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{143} & & \\ & V = \left\{ \frac{-16}{143} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{2})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 15x+\frac{15}{2}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x+ \frac{60}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{+60} & = & \color{red}{56x} +9 \\\Leftrightarrow & 120x \color{red}{+60} \color{blue}{-60} \color{blue}{-56x} & = & \color{red}{56x} +9 \color{blue}{-56x} \color{blue}{-60} \\\Leftrightarrow & 120x-56x& = & 9-60 \\\Leftrightarrow & \color{red}{64} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{64} & & \\ & V = \left\{ \frac{-51}{64} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{100x} +25 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +25 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & -240x-100x& = & 25-48 \\\Leftrightarrow & \color{red}{-340} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-340} & & \\\Leftrightarrow & x = \frac{23}{340} & & \\ & V = \left\{ \frac{23}{340} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{9})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 16x-\frac{16}{9}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{176}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-176} & = & \color{red}{891x} +45 \\\Leftrightarrow & 1584x \color{red}{-176} \color{blue}{+176} \color{blue}{-891x} & = & \color{red}{891x} +45 \color{blue}{-891x} \color{blue}{+176} \\\Leftrightarrow & 1584x-891x& = & 45+176 \\\Leftrightarrow & \color{red}{693} x& = & 221 \\\Leftrightarrow & x = \frac{221}{693} & & \\ & V = \left\{ \frac{221}{693} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{35x} +4 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & -168x-35x& = & 4-30 \\\Leftrightarrow & \color{red}{-203} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-203} & & \\\Leftrightarrow & x = \frac{26}{203} & & \\ & V = \left\{ \frac{26}{203} \right\} & \\\end{align}\)
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