Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+45} & = & \color{red}{-42x} +28 \\\Leftrightarrow & 315x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +28 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & 315x+42x& = & 28-45 \\\Leftrightarrow & \color{red}{357} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{357} & & \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 4x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+66} & = & \color{red}{308x} +49 \\\Leftrightarrow & -1155x \color{red}{+66} \color{blue}{-66} \color{blue}{-308x} & = & \color{red}{308x} +49 \color{blue}{-308x} \color{blue}{-66} \\\Leftrightarrow & -1155x-308x& = & 49-66 \\\Leftrightarrow & \color{red}{-1463} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1463} & & \\\Leftrightarrow & x = \frac{17}{1463} & & \\ & V = \left\{ \frac{17}{1463} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+54} & = & \color{red}{231x} +88 \\\Leftrightarrow & 792x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & 792x-231x& = & 88-54 \\\Leftrightarrow & \color{red}{561} x& = & 34 \\\Leftrightarrow & x = \frac{34}{561} & & \\\Leftrightarrow & x = \frac{2}{33} & & \\ & V = \left\{ \frac{2}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -18x-\frac{12}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-108} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1782x \color{red}{-108} \color{blue}{+108} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+108} \\\Leftrightarrow & -1782x-495x& = & 88+108 \\\Leftrightarrow & \color{red}{-2277} x& = & 196 \\\Leftrightarrow & x = \frac{196}{-2277} & & \\\Leftrightarrow & x = \frac{-196}{2277} & & \\ & V = \left\{ \frac{-196}{2277} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+8} & = & \color{red}{-30x} +15 \\\Leftrightarrow & 80x \color{red}{+8} \color{blue}{-8} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{-8} \\\Leftrightarrow & 80x+30x& = & 15-8 \\\Leftrightarrow & \color{red}{110} x& = & 7 \\\Leftrightarrow & x = \frac{7}{110} & & \\ & V = \left\{ \frac{7}{110} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{135x} +6 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{-20} \\\Leftrightarrow & -60x-135x& = & 6-20 \\\Leftrightarrow & \color{red}{-195} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-195} & & \\\Leftrightarrow & x = \frac{14}{195} & & \\ & V = \left\{ \frac{14}{195} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{6}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+24} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & -336x-140x& = & 63-24 \\\Leftrightarrow & \color{red}{-476} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-476} & & \\\Leftrightarrow & x = \frac{-39}{476} & & \\ & V = \left\{ \frac{-39}{476} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -14x+\frac{28}{3}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+28} & = & \color{red}{9x} +5 \\\Leftrightarrow & -42x \color{red}{+28} \color{blue}{-28} \color{blue}{-9x} & = & \color{red}{9x} +5 \color{blue}{-9x} \color{blue}{-28} \\\Leftrightarrow & -42x-9x& = & 5-28 \\\Leftrightarrow & \color{red}{-51} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-51} & & \\\Leftrightarrow & x = \frac{23}{51} & & \\ & V = \left\{ \frac{23}{51} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{12})& = & -4x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{25}{12}& = & -4x+\frac{8}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-900}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{-240}{ \color{blue}{60} }x+ \frac{96}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -900x \color{red}{-125} & = & \color{red}{-240x} +96 \\\Leftrightarrow & -900x \color{red}{-125} \color{blue}{+125} \color{blue}{+240x} & = & \color{red}{-240x} +96 \color{blue}{+240x} \color{blue}{+125} \\\Leftrightarrow & -900x+240x& = & 96+125 \\\Leftrightarrow & \color{red}{-660} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-660} & & \\\Leftrightarrow & x = \frac{-221}{660} & & \\ & V = \left\{ \frac{-221}{660} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{756}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 756x \color{red}{+180} & = & \color{red}{210x} +35 \\\Leftrightarrow & 756x \color{red}{+180} \color{blue}{-180} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{-180} \\\Leftrightarrow & 756x-210x& = & 35-180 \\\Leftrightarrow & \color{red}{546} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{546} & & \\ & V = \left\{ \frac{-145}{546} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-375}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -375x \color{red}{+100} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -375x \color{red}{+100} \color{blue}{-100} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-100} \\\Leftrightarrow & -375x+135x& = & 18-100 \\\Leftrightarrow & \color{red}{-240} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-240} & & \\\Leftrightarrow & x = \frac{41}{120} & & \\ & V = \left\{ \frac{41}{120} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{8})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1440}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1440x \color{red}{-135} & = & \color{red}{504x} +32 \\\Leftrightarrow & 1440x \color{red}{-135} \color{blue}{+135} \color{blue}{-504x} & = & \color{red}{504x} +32 \color{blue}{-504x} \color{blue}{+135} \\\Leftrightarrow & 1440x-504x& = & 32+135 \\\Leftrightarrow & \color{red}{936} x& = & 167 \\\Leftrightarrow & x = \frac{167}{936} & & \\ & V = \left\{ \frac{167}{936} \right\} & \\\end{align}\)
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