Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{5})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 6x+\frac{9}{5}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+9} & = & \color{red}{-25x} +3 \\\Leftrightarrow & 30x \color{red}{+9} \color{blue}{-9} \color{blue}{+25x} & = & \color{red}{-25x} +3 \color{blue}{+25x} \color{blue}{-9} \\\Leftrightarrow & 30x+25x& = & 3-9 \\\Leftrightarrow & \color{red}{55} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-32} & = & \color{red}{132x} +33 \\\Leftrightarrow & 440x \color{red}{-32} \color{blue}{+32} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{+32} \\\Leftrightarrow & 440x-132x& = & 33+32 \\\Leftrightarrow & \color{red}{308} x& = & 65 \\\Leftrightarrow & x = \frac{65}{308} & & \\ & V = \left\{ \frac{65}{308} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -210x+147x& = & 14+18 \\\Leftrightarrow & \color{red}{-63} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-63} & & \\\Leftrightarrow & x = \frac{-32}{63} & & \\ & V = \left\{ \frac{-32}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{5})& = & -3x+\frac{7}{5} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+14} & = & \color{red}{-15x} +7 \\\Leftrightarrow & -70x \color{red}{+14} \color{blue}{-14} \color{blue}{+15x} & = & \color{red}{-15x} +7 \color{blue}{+15x} \color{blue}{-14} \\\Leftrightarrow & -70x+15x& = & 7-14 \\\Leftrightarrow & \color{red}{-55} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-55} & & \\\Leftrightarrow & x = \frac{7}{55} & & \\ & V = \left\{ \frac{7}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{3})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+100} & = & \color{red}{135x} +27 \\\Leftrightarrow & -300x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +27 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & -300x-135x& = & 27-100 \\\Leftrightarrow & \color{red}{-435} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-435} & & \\\Leftrightarrow & x = \frac{73}{435} & & \\ & V = \left\{ \frac{73}{435} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{105x} +25 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -240x-105x& = & 25-36 \\\Leftrightarrow & \color{red}{-345} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-345} & & \\\Leftrightarrow & x = \frac{11}{345} & & \\ & V = \left\{ \frac{11}{345} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{10})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{9}{10}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{40}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{+99} & = & \color{red}{-880x} +40 \\\Leftrightarrow & -1650x \color{red}{+99} \color{blue}{-99} \color{blue}{+880x} & = & \color{red}{-880x} +40 \color{blue}{+880x} \color{blue}{-99} \\\Leftrightarrow & -1650x+880x& = & 40-99 \\\Leftrightarrow & \color{red}{-770} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-770} & & \\\Leftrightarrow & x = \frac{59}{770} & & \\ & V = \left\{ \frac{59}{770} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{8})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{25}{8}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x+ \frac{175}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{+175} & = & \color{red}{448x} +80 \\\Leftrightarrow & -840x \color{red}{+175} \color{blue}{-175} \color{blue}{-448x} & = & \color{red}{448x} +80 \color{blue}{-448x} \color{blue}{-175} \\\Leftrightarrow & -840x-448x& = & 80-175 \\\Leftrightarrow & \color{red}{-1288} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-1288} & & \\\Leftrightarrow & x = \frac{95}{1288} & & \\ & V = \left\{ \frac{95}{1288} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -6x+\frac{10}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+50} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -330x \color{red}{+50} \color{blue}{-50} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-50} \\\Leftrightarrow & -330x+385x& = & 33-50 \\\Leftrightarrow & \color{red}{55} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{55} & & \\ & V = \left\{ \frac{-17}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{20}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1056}{ \color{blue}{66} }x+ \frac{120}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1056x \color{red}{+120} & = & \color{red}{-462x} +77 \\\Leftrightarrow & -1056x \color{red}{+120} \color{blue}{-120} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{-120} \\\Leftrightarrow & -1056x+462x& = & 77-120 \\\Leftrightarrow & \color{red}{-594} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-594} & & \\\Leftrightarrow & x = \frac{43}{594} & & \\ & V = \left\{ \frac{43}{594} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{7})& = & 9x+\frac{5}{12} \\\Leftrightarrow & 8x-\frac{12}{7}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{672}{ \color{blue}{84} }x- \frac{144}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 672x \color{red}{-144} & = & \color{red}{756x} +35 \\\Leftrightarrow & 672x \color{red}{-144} \color{blue}{+144} \color{blue}{-756x} & = & \color{red}{756x} +35 \color{blue}{-756x} \color{blue}{+144} \\\Leftrightarrow & 672x-756x& = & 35+144 \\\Leftrightarrow & \color{red}{-84} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-84} & & \\\Leftrightarrow & x = \frac{-179}{84} & & \\ & V = \left\{ \frac{-179}{84} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{18x} +9 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & 120x-18x& = & 9+40 \\\Leftrightarrow & \color{red}{102} x& = & 49 \\\Leftrightarrow & x = \frac{49}{102} & & \\ & V = \left\{ \frac{49}{102} \right\} & \\\end{align}\)
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