Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{11})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{25}{11}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+125} & = & \color{red}{-495x} +66 \\\Leftrightarrow & -1100x \color{red}{+125} \color{blue}{-125} \color{blue}{+495x} & = & \color{red}{-495x} +66 \color{blue}{+495x} \color{blue}{-125} \\\Leftrightarrow & -1100x+495x& = & 66-125 \\\Leftrightarrow & \color{red}{-605} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-605} & & \\\Leftrightarrow & x = \frac{59}{605} & & \\ & V = \left\{ \frac{59}{605} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{-16} & = & \color{red}{21x} +6 \\\Leftrightarrow & 112x \color{red}{-16} \color{blue}{+16} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{+16} \\\Leftrightarrow & 112x-21x& = & 6+16 \\\Leftrightarrow & \color{red}{91} x& = & 22 \\\Leftrightarrow & x = \frac{22}{91} & & \\ & V = \left\{ \frac{22}{91} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+24} & = & \color{red}{45x} +8 \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-24} \\\Leftrightarrow & -36x-45x& = & 8-24 \\\Leftrightarrow & \color{red}{-81} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-81} & & \\\Leftrightarrow & x = \frac{16}{81} & & \\ & V = \left\{ \frac{16}{81} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{9})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-567x} +90 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+567x} & = & \color{red}{-567x} +90 \color{blue}{+567x} \color{blue}{+28} \\\Leftrightarrow & -252x+567x& = & 90+28 \\\Leftrightarrow & \color{red}{315} x& = & 118 \\\Leftrightarrow & x = \frac{118}{315} & & \\ & V = \left\{ \frac{118}{315} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{9}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{70x} +35 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & -60x-70x& = & 35+18 \\\Leftrightarrow & \color{red}{-130} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-130} & & \\\Leftrightarrow & x = \frac{-53}{130} & & \\ & V = \left\{ \frac{-53}{130} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+176} & = & \color{red}{385x} +28 \\\Leftrightarrow & -924x \color{red}{+176} \color{blue}{-176} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-176} \\\Leftrightarrow & -924x-385x& = & 28-176 \\\Leftrightarrow & \color{red}{-1309} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-1309} & & \\\Leftrightarrow & x = \frac{148}{1309} & & \\ & V = \left\{ \frac{148}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{28}{5}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-84} & = & \color{red}{30x} +20 \\\Leftrightarrow & 315x \color{red}{-84} \color{blue}{+84} \color{blue}{-30x} & = & \color{red}{30x} +20 \color{blue}{-30x} \color{blue}{+84} \\\Leftrightarrow & 315x-30x& = & 20+84 \\\Leftrightarrow & \color{red}{285} x& = & 104 \\\Leftrightarrow & x = \frac{104}{285} & & \\ & V = \left\{ \frac{104}{285} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{5})& = & -3x+\frac{5}{4} \\\Leftrightarrow & 28x+\frac{14}{5}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{560}{ \color{blue}{20} }x+ \frac{56}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 560x \color{red}{+56} & = & \color{red}{-60x} +25 \\\Leftrightarrow & 560x \color{red}{+56} \color{blue}{-56} \color{blue}{+60x} & = & \color{red}{-60x} +25 \color{blue}{+60x} \color{blue}{-56} \\\Leftrightarrow & 560x+60x& = & 25-56 \\\Leftrightarrow & \color{red}{620} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{620} & & \\\Leftrightarrow & x = \frac{-1}{20} & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{9})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{25}{9}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-275} & = & \color{red}{-693x} +18 \\\Leftrightarrow & -990x \color{red}{-275} \color{blue}{+275} \color{blue}{+693x} & = & \color{red}{-693x} +18 \color{blue}{+693x} \color{blue}{+275} \\\Leftrightarrow & -990x+693x& = & 18+275 \\\Leftrightarrow & \color{red}{-297} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-297} & & \\\Leftrightarrow & x = \frac{-293}{297} & & \\ & V = \left\{ \frac{-293}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{+180} & = & \color{red}{-770x} +77 \\\Leftrightarrow & -3300x \color{red}{+180} \color{blue}{-180} \color{blue}{+770x} & = & \color{red}{-770x} +77 \color{blue}{+770x} \color{blue}{-180} \\\Leftrightarrow & -3300x+770x& = & 77-180 \\\Leftrightarrow & \color{red}{-2530} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-2530} & & \\\Leftrightarrow & x = \frac{103}{2530} & & \\ & V = \left\{ \frac{103}{2530} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +40 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 40+36 \\\Leftrightarrow & \color{red}{-255} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-255} & & \\\Leftrightarrow & x = \frac{-76}{255} & & \\ & V = \left\{ \frac{-76}{255} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{8})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{48x} +32 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{-48x} & = & \color{red}{48x} +32 \color{blue}{-48x} \color{blue}{+63} \\\Leftrightarrow & 504x-48x& = & 32+63 \\\Leftrightarrow & \color{red}{456} x& = & 95 \\\Leftrightarrow & x = \frac{95}{456} & & \\\Leftrightarrow & x = \frac{5}{24} & & \\ & V = \left\{ \frac{5}{24} \right\} & \\\end{align}\)
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