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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{7})& = & 9x+\frac{7}{6} \\\Leftrightarrow & -8x+\frac{8}{7}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{378x} +49 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{-378x} & = & \color{red}{378x} +49 \color{blue}{-378x} \color{blue}{-48} \\\Leftrightarrow & -336x-378x& = & 49-48 \\\Leftrightarrow & \color{red}{-714} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-714} & & \\\Leftrightarrow & x = \frac{-1}{714} & & \\ & V = \left\{ \frac{-1}{714} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+112} & = & \color{red}{539x} +88 \\\Leftrightarrow & 1232x \color{red}{+112} \color{blue}{-112} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-112} \\\Leftrightarrow & 1232x-539x& = & 88-112 \\\Leftrightarrow & \color{red}{693} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{693} & & \\\Leftrightarrow & x = \frac{-8}{231} & & \\ & V = \left\{ \frac{-8}{231} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{154x} +77 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{+60} \\\Leftrightarrow & -660x-154x& = & 77+60 \\\Leftrightarrow & \color{red}{-814} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-814} & & \\\Leftrightarrow & x = \frac{-137}{814} & & \\ & V = \left\{ \frac{-137}{814} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-216x} +20 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +20 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & 336x+216x& = & 20-63 \\\Leftrightarrow & \color{red}{552} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{552} & & \\ & V = \left\{ \frac{-43}{552} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{4})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -14x+\frac{35}{4}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x+ \frac{315}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+315} & = & \color{red}{-108x} +16 \\\Leftrightarrow & -504x \color{red}{+315} \color{blue}{-315} \color{blue}{+108x} & = & \color{red}{-108x} +16 \color{blue}{+108x} \color{blue}{-315} \\\Leftrightarrow & -504x+108x& = & 16-315 \\\Leftrightarrow & \color{red}{-396} x& = & -299 \\\Leftrightarrow & x = \frac{-299}{-396} & & \\\Leftrightarrow & x = \frac{299}{396} & & \\ & V = \left\{ \frac{299}{396} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{8}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-56} & = & \color{red}{441x} +90 \\\Leftrightarrow & -378x \color{red}{-56} \color{blue}{+56} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+56} \\\Leftrightarrow & -378x-441x& = & 90+56 \\\Leftrightarrow & \color{red}{-819} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-819} & & \\\Leftrightarrow & x = \frac{-146}{819} & & \\ & V = \left\{ \frac{-146}{819} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & 9x+\frac{7}{11} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{+10} & = & \color{red}{99x} +7 \\\Leftrightarrow & 44x \color{red}{+10} \color{blue}{-10} \color{blue}{-99x} & = & \color{red}{99x} +7 \color{blue}{-99x} \color{blue}{-10} \\\Leftrightarrow & 44x-99x& = & 7-10 \\\Leftrightarrow & \color{red}{-55} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-55} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{4})& = & 2x+\frac{3}{11} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{-165} & = & \color{red}{88x} +12 \\\Leftrightarrow & -1100x \color{red}{-165} \color{blue}{+165} \color{blue}{-88x} & = & \color{red}{88x} +12 \color{blue}{-88x} \color{blue}{+165} \\\Leftrightarrow & -1100x-88x& = & 12+165 \\\Leftrightarrow & \color{red}{-1188} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-1188} & & \\\Leftrightarrow & x = \frac{-59}{396} & & \\ & V = \left\{ \frac{-59}{396} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{4})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-45} & = & \color{red}{24x} +16 \\\Leftrightarrow & 300x \color{red}{-45} \color{blue}{+45} \color{blue}{-24x} & = & \color{red}{24x} +16 \color{blue}{-24x} \color{blue}{+45} \\\Leftrightarrow & 300x-24x& = & 16+45 \\\Leftrightarrow & \color{red}{276} x& = & 61 \\\Leftrightarrow & x = \frac{61}{276} & & \\ & V = \left\{ \frac{61}{276} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1323}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1323x \color{red}{-98} & = & \color{red}{504x} +90 \\\Leftrightarrow & -1323x \color{red}{-98} \color{blue}{+98} \color{blue}{-504x} & = & \color{red}{504x} +90 \color{blue}{-504x} \color{blue}{+98} \\\Leftrightarrow & -1323x-504x& = & 90+98 \\\Leftrightarrow & \color{red}{-1827} x& = & 188 \\\Leftrightarrow & x = \frac{188}{-1827} & & \\\Leftrightarrow & x = \frac{-188}{1827} & & \\ & V = \left\{ \frac{-188}{1827} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{11})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 16x-\frac{16}{11}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-112} & = & \color{red}{231x} +66 \\\Leftrightarrow & 1232x \color{red}{-112} \color{blue}{+112} \color{blue}{-231x} & = & \color{red}{231x} +66 \color{blue}{-231x} \color{blue}{+112} \\\Leftrightarrow & 1232x-231x& = & 66+112 \\\Leftrightarrow & \color{red}{1001} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1001} & & \\ & V = \left\{ \frac{178}{1001} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & 6x+\frac{3}{4} \\\Leftrightarrow & -25x+\frac{10}{3}& = & 6x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+40} & = & \color{red}{72x} +9 \\\Leftrightarrow & -300x \color{red}{+40} \color{blue}{-40} \color{blue}{-72x} & = & \color{red}{72x} +9 \color{blue}{-72x} \color{blue}{-40} \\\Leftrightarrow & -300x-72x& = & 9-40 \\\Leftrightarrow & \color{red}{-372} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-372} & & \\\Leftrightarrow & x = \frac{1}{12} & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
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