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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +110 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 110-54 \\\Leftrightarrow & \color{red}{-1221} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-1221} & & \\\Leftrightarrow & x = \frac{-56}{1221} & & \\ & V = \left\{ \frac{-56}{1221} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{200x} +15 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & 480x-200x& = & 15-96 \\\Leftrightarrow & \color{red}{280} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{280} & & \\ & V = \left\{ \frac{-81}{280} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 28+18 \\\Leftrightarrow & \color{red}{21} x& = & 46 \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{8})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -14x-\frac{35}{8}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x- \frac{245}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{-245} & = & \color{red}{-168x} +80 \\\Leftrightarrow & -784x \color{red}{-245} \color{blue}{+245} \color{blue}{+168x} & = & \color{red}{-168x} +80 \color{blue}{+168x} \color{blue}{+245} \\\Leftrightarrow & -784x+168x& = & 80+245 \\\Leftrightarrow & \color{red}{-616} x& = & 325 \\\Leftrightarrow & x = \frac{325}{-616} & & \\\Leftrightarrow & x = \frac{-325}{616} & & \\ & V = \left\{ \frac{-325}{616} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{5})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -24x+\frac{18}{5}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{35x} +7 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +7 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & -120x-35x& = & 7-18 \\\Leftrightarrow & \color{red}{-155} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-155} & & \\\Leftrightarrow & x = \frac{11}{155} & & \\ & V = \left\{ \frac{11}{155} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-270} & = & \color{red}{495x} +110 \\\Leftrightarrow & 2376x \color{red}{-270} \color{blue}{+270} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+270} \\\Leftrightarrow & 2376x-495x& = & 110+270 \\\Leftrightarrow & \color{red}{1881} x& = & 380 \\\Leftrightarrow & x = \frac{380}{1881} & & \\\Leftrightarrow & x = \frac{20}{99} & & \\ & V = \left\{ \frac{20}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{384}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 384x \color{red}{-64} & = & \color{red}{-216x} +9 \\\Leftrightarrow & 384x \color{red}{-64} \color{blue}{+64} \color{blue}{+216x} & = & \color{red}{-216x} +9 \color{blue}{+216x} \color{blue}{+64} \\\Leftrightarrow & 384x+216x& = & 9+64 \\\Leftrightarrow & \color{red}{600} x& = & 73 \\\Leftrightarrow & x = \frac{73}{600} & & \\ & V = \left\{ \frac{73}{600} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{-108} & = & \color{red}{693x} +110 \\\Leftrightarrow & 1485x \color{red}{-108} \color{blue}{+108} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+108} \\\Leftrightarrow & 1485x-693x& = & 110+108 \\\Leftrightarrow & \color{red}{792} x& = & 218 \\\Leftrightarrow & x = \frac{218}{792} & & \\\Leftrightarrow & x = \frac{109}{396} & & \\ & V = \left\{ \frac{109}{396} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-30} \\\Leftrightarrow & 420x+63x& = & 14-30 \\\Leftrightarrow & \color{red}{483} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{483} & & \\ & V = \left\{ \frac{-16}{483} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{4})& = & 4x+\frac{8}{9} \\\Leftrightarrow & 35x-\frac{35}{4}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{-315} & = & \color{red}{144x} +32 \\\Leftrightarrow & 1260x \color{red}{-315} \color{blue}{+315} \color{blue}{-144x} & = & \color{red}{144x} +32 \color{blue}{-144x} \color{blue}{+315} \\\Leftrightarrow & 1260x-144x& = & 32+315 \\\Leftrightarrow & \color{red}{1116} x& = & 347 \\\Leftrightarrow & x = \frac{347}{1116} & & \\ & V = \left\{ \frac{347}{1116} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+80} & = & \color{red}{105x} +42 \\\Leftrightarrow & 280x \color{red}{+80} \color{blue}{-80} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{-80} \\\Leftrightarrow & 280x-105x& = & 42-80 \\\Leftrightarrow & \color{red}{175} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{175} & & \\ & V = \left\{ \frac{-38}{175} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+75} & = & \color{red}{385x} +66 \\\Leftrightarrow & -330x \color{red}{+75} \color{blue}{-75} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-75} \\\Leftrightarrow & -330x-385x& = & 66-75 \\\Leftrightarrow & \color{red}{-715} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-715} & & \\\Leftrightarrow & x = \frac{9}{715} & & \\ & V = \left\{ \frac{9}{715} \right\} & \\\end{align}\)
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