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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+44} & = & \color{red}{-495x} +50 \\\Leftrightarrow & -440x \color{red}{+44} \color{blue}{-44} \color{blue}{+495x} & = & \color{red}{-495x} +50 \color{blue}{+495x} \color{blue}{-44} \\\Leftrightarrow & -440x+495x& = & 50-44 \\\Leftrightarrow & \color{red}{55} x& = & 6 \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{50x} +35 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & -90x-50x& = & 35-24 \\\Leftrightarrow & \color{red}{-140} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-140} & & \\\Leftrightarrow & x = \frac{-11}{140} & & \\ & V = \left\{ \frac{-11}{140} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{5})& = & 6x+\frac{8}{11} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 6x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{-154} & = & \color{red}{330x} +40 \\\Leftrightarrow & 1925x \color{red}{-154} \color{blue}{+154} \color{blue}{-330x} & = & \color{red}{330x} +40 \color{blue}{-330x} \color{blue}{+154} \\\Leftrightarrow & 1925x-330x& = & 40+154 \\\Leftrightarrow & \color{red}{1595} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1595} & & \\ & V = \left\{ \frac{194}{1595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{5})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 14x-\frac{14}{5}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{-30x} +7 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{+28} \\\Leftrightarrow & 140x+30x& = & 7+28 \\\Leftrightarrow & \color{red}{170} x& = & 35 \\\Leftrightarrow & x = \frac{35}{170} & & \\\Leftrightarrow & x = \frac{7}{34} & & \\ & V = \left\{ \frac{7}{34} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{11})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{10}{11}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+50} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -440x \color{red}{+50} \color{blue}{-50} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-50} \\\Leftrightarrow & -440x+165x& = & 44-50 \\\Leftrightarrow & \color{red}{-275} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-275} & & \\\Leftrightarrow & x = \frac{6}{275} & & \\ & V = \left\{ \frac{6}{275} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{-8} & = & \color{red}{-70x} +25 \\\Leftrightarrow & 40x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & 40x+70x& = & 25+8 \\\Leftrightarrow & \color{red}{110} x& = & 33 \\\Leftrightarrow & x = \frac{33}{110} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{7})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-176} & = & \color{red}{-231x} +70 \\\Leftrightarrow & 1232x \color{red}{-176} \color{blue}{+176} \color{blue}{+231x} & = & \color{red}{-231x} +70 \color{blue}{+231x} \color{blue}{+176} \\\Leftrightarrow & 1232x+231x& = & 70+176 \\\Leftrightarrow & \color{red}{1463} x& = & 246 \\\Leftrightarrow & x = \frac{246}{1463} & & \\ & V = \left\{ \frac{246}{1463} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -4x-\frac{6}{5}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-66} & = & \color{red}{495x} +45 \\\Leftrightarrow & -220x \color{red}{-66} \color{blue}{+66} \color{blue}{-495x} & = & \color{red}{495x} +45 \color{blue}{-495x} \color{blue}{+66} \\\Leftrightarrow & -220x-495x& = & 45+66 \\\Leftrightarrow & \color{red}{-715} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-715} & & \\\Leftrightarrow & x = \frac{-111}{715} & & \\ & V = \left\{ \frac{-111}{715} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{9})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{-20} & = & \color{red}{315x} +63 \\\Leftrightarrow & 450x \color{red}{-20} \color{blue}{+20} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{+20} \\\Leftrightarrow & 450x-315x& = & 63+20 \\\Leftrightarrow & \color{red}{135} x& = & 83 \\\Leftrightarrow & x = \frac{83}{135} & & \\ & V = \left\{ \frac{83}{135} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{-30} & = & \color{red}{55x} +8 \\\Leftrightarrow & 264x \color{red}{-30} \color{blue}{+30} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{+30} \\\Leftrightarrow & 264x-55x& = & 8+30 \\\Leftrightarrow & \color{red}{209} x& = & 38 \\\Leftrightarrow & x = \frac{38}{209} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 21x-\frac{14}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-50x} +3 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{+28} \\\Leftrightarrow & 210x+50x& = & 3+28 \\\Leftrightarrow & \color{red}{260} x& = & 31 \\\Leftrightarrow & x = \frac{31}{260} & & \\ & V = \left\{ \frac{31}{260} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 8x+\frac{5}{6} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{-72} & = & \color{red}{240x} +25 \\\Leftrightarrow & -450x \color{red}{-72} \color{blue}{+72} \color{blue}{-240x} & = & \color{red}{240x} +25 \color{blue}{-240x} \color{blue}{+72} \\\Leftrightarrow & -450x-240x& = & 25+72 \\\Leftrightarrow & \color{red}{-690} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-690} & & \\\Leftrightarrow & x = \frac{-97}{690} & & \\ & V = \left\{ \frac{-97}{690} \right\} & \\\end{align}\)
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