Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & 9x+\frac{5}{4} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 9x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{252x} +35 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-252x} & = & \color{red}{252x} +35 \color{blue}{-252x} \color{blue}{-40} \\\Leftrightarrow & 280x-252x& = & 35-40 \\\Leftrightarrow & \color{red}{28} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{28} & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{9})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{20}{9}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+140} & = & \color{red}{-315x} +90 \\\Leftrightarrow & 756x \color{red}{+140} \color{blue}{-140} \color{blue}{+315x} & = & \color{red}{-315x} +90 \color{blue}{+315x} \color{blue}{-140} \\\Leftrightarrow & 756x+315x& = & 90-140 \\\Leftrightarrow & \color{red}{1071} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{1071} & & \\ & V = \left\{ \frac{-50}{1071} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -8x+\frac{10}{9}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{+40} & = & \color{red}{324x} +27 \\\Leftrightarrow & -288x \color{red}{+40} \color{blue}{-40} \color{blue}{-324x} & = & \color{red}{324x} +27 \color{blue}{-324x} \color{blue}{-40} \\\Leftrightarrow & -288x-324x& = & 27-40 \\\Leftrightarrow & \color{red}{-612} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-612} & & \\\Leftrightarrow & x = \frac{13}{612} & & \\ & V = \left\{ \frac{13}{612} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+126} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 924x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & 924x+385x& = & 110-126 \\\Leftrightarrow & \color{red}{1309} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{1309} & & \\ & V = \left\{ \frac{-16}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{+80} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 144x \color{red}{+80} \color{blue}{-80} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{-80} \\\Leftrightarrow & 144x+60x& = & 27-80 \\\Leftrightarrow & \color{red}{204} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{204} & & \\ & V = \left\{ \frac{-53}{204} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{8}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{120}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 120x \color{red}{-80} & = & \color{red}{270x} +27 \\\Leftrightarrow & 120x \color{red}{-80} \color{blue}{+80} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+80} \\\Leftrightarrow & 120x-270x& = & 27+80 \\\Leftrightarrow & \color{red}{-150} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-150} & & \\\Leftrightarrow & x = \frac{-107}{150} & & \\ & V = \left\{ \frac{-107}{150} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{7})& = & 9x+\frac{9}{8} \\\Leftrightarrow & -8x-\frac{8}{7}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x- \frac{64}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{-64} & = & \color{red}{504x} +63 \\\Leftrightarrow & -448x \color{red}{-64} \color{blue}{+64} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{+64} \\\Leftrightarrow & -448x-504x& = & 63+64 \\\Leftrightarrow & \color{red}{-952} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-952} & & \\\Leftrightarrow & x = \frac{-127}{952} & & \\ & V = \left\{ \frac{-127}{952} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{1}{3})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{7}{3}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{49}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-49} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 441x \color{red}{-49} \color{blue}{+49} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{+49} \\\Leftrightarrow & 441x+42x& = & 27+49 \\\Leftrightarrow & \color{red}{483} x& = & 76 \\\Leftrightarrow & x = \frac{76}{483} & & \\ & V = \left\{ \frac{76}{483} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & 9x+\frac{3}{11} \\\Leftrightarrow & 14x-\frac{21}{2}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{308}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{6}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 308x \color{red}{-231} & = & \color{red}{198x} +6 \\\Leftrightarrow & 308x \color{red}{-231} \color{blue}{+231} \color{blue}{-198x} & = & \color{red}{198x} +6 \color{blue}{-198x} \color{blue}{+231} \\\Leftrightarrow & 308x-198x& = & 6+231 \\\Leftrightarrow & \color{red}{110} x& = & 237 \\\Leftrightarrow & x = \frac{237}{110} & & \\ & V = \left\{ \frac{237}{110} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{-25x} +2 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 90x+25x& = & 2+12 \\\Leftrightarrow & \color{red}{115} x& = & 14 \\\Leftrightarrow & x = \frac{14}{115} & & \\ & V = \left\{ \frac{14}{115} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{-30x} +15 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{+24} \\\Leftrightarrow & 200x+30x& = & 15+24 \\\Leftrightarrow & \color{red}{230} x& = & 39 \\\Leftrightarrow & x = \frac{39}{230} & & \\ & V = \left\{ \frac{39}{230} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-63} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -315x \color{red}{-63} \color{blue}{+63} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+63} \\\Leftrightarrow & -315x+175x& = & 20+63 \\\Leftrightarrow & \color{red}{-140} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-140} & & \\\Leftrightarrow & x = \frac{-83}{140} & & \\ & V = \left\{ \frac{-83}{140} \right\} & \\\end{align}\)
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