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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{-12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & 100x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 100x+35x& = & 7+12 \\\Leftrightarrow & \color{red}{135} x& = & 19 \\\Leftrightarrow & x = \frac{19}{135} & & \\ & V = \left\{ \frac{19}{135} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{9}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{9}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-9} & = & \color{red}{-56x} +36 \\\Leftrightarrow & 120x \color{red}{-9} \color{blue}{+9} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{+9} \\\Leftrightarrow & 120x+56x& = & 36+9 \\\Leftrightarrow & \color{red}{176} x& = & 45 \\\Leftrightarrow & x = \frac{45}{176} & & \\ & V = \left\{ \frac{45}{176} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-44} & = & \color{red}{495x} +50 \\\Leftrightarrow & 220x \color{red}{-44} \color{blue}{+44} \color{blue}{-495x} & = & \color{red}{495x} +50 \color{blue}{-495x} \color{blue}{+44} \\\Leftrightarrow & 220x-495x& = & 50+44 \\\Leftrightarrow & \color{red}{-275} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-275} & & \\\Leftrightarrow & x = \frac{-94}{275} & & \\ & V = \left\{ \frac{-94}{275} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 594x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{363} x& = & 164 \\\Leftrightarrow & x = \frac{164}{363} & & \\ & V = \left\{ \frac{164}{363} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-44} & = & \color{red}{-495x} +10 \\\Leftrightarrow & 440x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +10 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & 440x+495x& = & 10+44 \\\Leftrightarrow & \color{red}{935} x& = & 54 \\\Leftrightarrow & x = \frac{54}{935} & & \\ & V = \left\{ \frac{54}{935} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1680x \color{red}{-192} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -1680x \color{red}{-192} \color{blue}{+192} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+192} \\\Leftrightarrow & -1680x+588x& = & 35+192 \\\Leftrightarrow & \color{red}{-1092} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-1092} & & \\\Leftrightarrow & x = \frac{-227}{1092} & & \\ & V = \left\{ \frac{-227}{1092} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{8})& = & 2x+\frac{9}{8} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{+21} & = & \color{red}{16x} +9 \\\Leftrightarrow & 280x \color{red}{+21} \color{blue}{-21} \color{blue}{-16x} & = & \color{red}{16x} +9 \color{blue}{-16x} \color{blue}{-21} \\\Leftrightarrow & 280x-16x& = & 9-21 \\\Leftrightarrow & \color{red}{264} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{264} & & \\\Leftrightarrow & x = \frac{-1}{22} & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & 8x+\frac{7}{9} \\\Leftrightarrow & -18x-\frac{24}{11}& = & 8x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-216} & = & \color{red}{792x} +77 \\\Leftrightarrow & -1782x \color{red}{-216} \color{blue}{+216} \color{blue}{-792x} & = & \color{red}{792x} +77 \color{blue}{-792x} \color{blue}{+216} \\\Leftrightarrow & -1782x-792x& = & 77+216 \\\Leftrightarrow & \color{red}{-2574} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-2574} & & \\\Leftrightarrow & x = \frac{-293}{2574} & & \\ & V = \left\{ \frac{-293}{2574} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{-72} & = & \color{red}{-220x} +77 \\\Leftrightarrow & -1056x \color{red}{-72} \color{blue}{+72} \color{blue}{+220x} & = & \color{red}{-220x} +77 \color{blue}{+220x} \color{blue}{+72} \\\Leftrightarrow & -1056x+220x& = & 77+72 \\\Leftrightarrow & \color{red}{-836} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-836} & & \\\Leftrightarrow & x = \frac{-149}{836} & & \\ & V = \left\{ \frac{-149}{836} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 252x-105x& = & 56+18 \\\Leftrightarrow & \color{red}{147} x& = & 74 \\\Leftrightarrow & x = \frac{74}{147} & & \\ & V = \left\{ \frac{74}{147} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{11})& = & -8x+\frac{4}{5} \\\Leftrightarrow & 25x+\frac{20}{11}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{+100} & = & \color{red}{-440x} +44 \\\Leftrightarrow & 1375x \color{red}{+100} \color{blue}{-100} \color{blue}{+440x} & = & \color{red}{-440x} +44 \color{blue}{+440x} \color{blue}{-100} \\\Leftrightarrow & 1375x+440x& = & 44-100 \\\Leftrightarrow & \color{red}{1815} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{1815} & & \\ & V = \left\{ \frac{-56}{1815} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -16x+\frac{16}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+16} & = & \color{red}{-77x} +2 \\\Leftrightarrow & -176x \color{red}{+16} \color{blue}{-16} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-16} \\\Leftrightarrow & -176x+77x& = & 2-16 \\\Leftrightarrow & \color{red}{-99} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-99} & & \\\Leftrightarrow & x = \frac{14}{99} & & \\ & V = \left\{ \frac{14}{99} \right\} & \\\end{align}\)
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