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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-30} & = & \color{red}{105x} +42 \\\Leftrightarrow & 350x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 350x-105x& = & 42+30 \\\Leftrightarrow & \color{red}{245} x& = & 72 \\\Leftrightarrow & x = \frac{72}{245} & & \\ & V = \left\{ \frac{72}{245} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & -4x+\frac{10}{9} \\\Leftrightarrow & -15x+\frac{20}{11}& = & -4x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x+ \frac{180}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{+180} & = & \color{red}{-396x} +110 \\\Leftrightarrow & -1485x \color{red}{+180} \color{blue}{-180} \color{blue}{+396x} & = & \color{red}{-396x} +110 \color{blue}{+396x} \color{blue}{-180} \\\Leftrightarrow & -1485x+396x& = & 110-180 \\\Leftrightarrow & \color{red}{-1089} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-1089} & & \\\Leftrightarrow & x = \frac{70}{1089} & & \\ & V = \left\{ \frac{70}{1089} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{4})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 25x-\frac{25}{4}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{75}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{-24x} +8 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{+75} \\\Leftrightarrow & 300x+24x& = & 8+75 \\\Leftrightarrow & \color{red}{324} x& = & 83 \\\Leftrightarrow & x = \frac{83}{324} & & \\ & V = \left\{ \frac{83}{324} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{4})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{-140x} +16 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +16 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & 168x+140x& = & 16+105 \\\Leftrightarrow & \color{red}{308} x& = & 121 \\\Leftrightarrow & x = \frac{121}{308} & & \\\Leftrightarrow & x = \frac{11}{28} & & \\ & V = \left\{ \frac{11}{28} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{35x} +3 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & -84x-35x& = & 3-30 \\\Leftrightarrow & \color{red}{-119} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-119} & & \\\Leftrightarrow & x = \frac{27}{119} & & \\ & V = \left\{ \frac{27}{119} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{32x} +9 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +9 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & -60x-32x& = & 9+15 \\\Leftrightarrow & \color{red}{-92} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-92} & & \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -405x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -405x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{-90} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-90} & & \\\Leftrightarrow & x = \frac{29}{45} & & \\ & V = \left\{ \frac{29}{45} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{4}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+4} & = & \color{red}{63x} +6 \\\Leftrightarrow & 90x \color{red}{+4} \color{blue}{-4} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-4} \\\Leftrightarrow & 90x-63x& = & 6-4 \\\Leftrightarrow & \color{red}{27} x& = & 2 \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{15}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+165} & = & \color{red}{693x} +42 \\\Leftrightarrow & 770x \color{red}{+165} \color{blue}{-165} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-165} \\\Leftrightarrow & 770x-693x& = & 42-165 \\\Leftrightarrow & \color{red}{77} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{77} & & \\ & V = \left\{ \frac{-123}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{5})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -21x+\frac{14}{5}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1155}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{440x} +50 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-440x} & = & \color{red}{440x} +50 \color{blue}{-440x} \color{blue}{-154} \\\Leftrightarrow & -1155x-440x& = & 50-154 \\\Leftrightarrow & \color{red}{-1595} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1595} & & \\\Leftrightarrow & x = \frac{104}{1595} & & \\ & V = \left\{ \frac{104}{1595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{1}{2})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 35x-\frac{7}{2}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x- \frac{28}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{-28} & = & \color{red}{24x} +9 \\\Leftrightarrow & 280x \color{red}{-28} \color{blue}{+28} \color{blue}{-24x} & = & \color{red}{24x} +9 \color{blue}{-24x} \color{blue}{+28} \\\Leftrightarrow & 280x-24x& = & 9+28 \\\Leftrightarrow & \color{red}{256} x& = & 37 \\\Leftrightarrow & x = \frac{37}{256} & & \\ & V = \left\{ \frac{37}{256} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{28}{9}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{-56} & = & \color{red}{54x} +63 \\\Leftrightarrow & -630x \color{red}{-56} \color{blue}{+56} \color{blue}{-54x} & = & \color{red}{54x} +63 \color{blue}{-54x} \color{blue}{+56} \\\Leftrightarrow & -630x-54x& = & 63+56 \\\Leftrightarrow & \color{red}{-684} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-684} & & \\\Leftrightarrow & x = \frac{-119}{684} & & \\ & V = \left\{ \frac{-119}{684} \right\} & \\\end{align}\)
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