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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{210x} +9 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{-100} \\\Leftrightarrow & 240x-210x& = & 9-100 \\\Leftrightarrow & \color{red}{30} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{30} & & \\ & V = \left\{ \frac{-91}{30} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 4x+\frac{10}{11}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+90} & = & \color{red}{-891x} +110 \\\Leftrightarrow & 396x \color{red}{+90} \color{blue}{-90} \color{blue}{+891x} & = & \color{red}{-891x} +110 \color{blue}{+891x} \color{blue}{-90} \\\Leftrightarrow & 396x+891x& = & 110-90 \\\Leftrightarrow & \color{red}{1287} x& = & 20 \\\Leftrightarrow & x = \frac{20}{1287} & & \\ & V = \left\{ \frac{20}{1287} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{12}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+60} & = & \color{red}{385x} +44 \\\Leftrightarrow & 1100x \color{red}{+60} \color{blue}{-60} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-60} \\\Leftrightarrow & 1100x-385x& = & 44-60 \\\Leftrightarrow & \color{red}{715} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{715} & & \\ & V = \left\{ \frac{-16}{715} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-108} & = & \color{red}{315x} +50 \\\Leftrightarrow & -720x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -720x-315x& = & 50+108 \\\Leftrightarrow & \color{red}{-1035} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-1035} & & \\\Leftrightarrow & x = \frac{-158}{1035} & & \\ & V = \left\{ \frac{-158}{1035} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +45 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 45-132 \\\Leftrightarrow & \color{red}{-385} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-385} & & \\\Leftrightarrow & x = \frac{87}{385} & & \\ & V = \left\{ \frac{87}{385} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{11})& = & -8x+\frac{3}{8} \\\Leftrightarrow & 15x+\frac{12}{11}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{96}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+96} & = & \color{red}{-704x} +33 \\\Leftrightarrow & 1320x \color{red}{+96} \color{blue}{-96} \color{blue}{+704x} & = & \color{red}{-704x} +33 \color{blue}{+704x} \color{blue}{-96} \\\Leftrightarrow & 1320x+704x& = & 33-96 \\\Leftrightarrow & \color{red}{2024} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{2024} & & \\ & V = \left\{ \frac{-63}{2024} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{10}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{-20} & = & \color{red}{154x} +33 \\\Leftrightarrow & 132x \color{red}{-20} \color{blue}{+20} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+20} \\\Leftrightarrow & 132x-154x& = & 33+20 \\\Leftrightarrow & \color{red}{-22} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-22} & & \\\Leftrightarrow & x = \frac{-53}{22} & & \\ & V = \left\{ \frac{-53}{22} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{7})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 16x+\frac{12}{7}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1344}{ \color{blue}{84} }x+ \frac{144}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1344x \color{red}{+144} & = & \color{red}{756x} +49 \\\Leftrightarrow & 1344x \color{red}{+144} \color{blue}{-144} \color{blue}{-756x} & = & \color{red}{756x} +49 \color{blue}{-756x} \color{blue}{-144} \\\Leftrightarrow & 1344x-756x& = & 49-144 \\\Leftrightarrow & \color{red}{588} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{588} & & \\ & V = \left\{ \frac{-95}{588} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -35x-\frac{28}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-84} & = & \color{red}{135x} +10 \\\Leftrightarrow & -525x \color{red}{-84} \color{blue}{+84} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{+84} \\\Leftrightarrow & -525x-135x& = & 10+84 \\\Leftrightarrow & \color{red}{-660} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-660} & & \\\Leftrightarrow & x = \frac{-47}{330} & & \\ & V = \left\{ \frac{-47}{330} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{50x} +15 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-18} \\\Leftrightarrow & -120x-50x& = & 15-18 \\\Leftrightarrow & \color{red}{-170} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-170} & & \\\Leftrightarrow & x = \frac{3}{170} & & \\ & V = \left\{ \frac{3}{170} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{15}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+15} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{+15} \color{blue}{-15} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-15} \\\Leftrightarrow & -42x-49x& = & 10-15 \\\Leftrightarrow & \color{red}{-91} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-91} & & \\\Leftrightarrow & x = \frac{5}{91} & & \\ & V = \left\{ \frac{5}{91} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{-539x} +55 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{+42} \\\Leftrightarrow & -462x+539x& = & 55+42 \\\Leftrightarrow & \color{red}{77} x& = & 97 \\\Leftrightarrow & x = \frac{97}{77} & & \\ & V = \left\{ \frac{97}{77} \right\} & \\\end{align}\)
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