Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{9})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{25}{9}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{50}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-50} & = & \color{red}{126x} +45 \\\Leftrightarrow & -360x \color{red}{-50} \color{blue}{+50} \color{blue}{-126x} & = & \color{red}{126x} +45 \color{blue}{-126x} \color{blue}{+50} \\\Leftrightarrow & -360x-126x& = & 45+50 \\\Leftrightarrow & \color{red}{-486} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-486} & & \\\Leftrightarrow & x = \frac{-95}{486} & & \\ & V = \left\{ \frac{-95}{486} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1800}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1800x \color{red}{+144} & = & \color{red}{-420x} +25 \\\Leftrightarrow & -1800x \color{red}{+144} \color{blue}{-144} \color{blue}{+420x} & = & \color{red}{-420x} +25 \color{blue}{+420x} \color{blue}{-144} \\\Leftrightarrow & -1800x+420x& = & 25-144 \\\Leftrightarrow & \color{red}{-1380} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-1380} & & \\\Leftrightarrow & x = \frac{119}{1380} & & \\ & V = \left\{ \frac{119}{1380} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{63x} +6 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+56} \\\Leftrightarrow & 84x-63x& = & 6+56 \\\Leftrightarrow & \color{red}{21} x& = & 62 \\\Leftrightarrow & x = \frac{62}{21} & & \\ & V = \left\{ \frac{62}{21} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -14x+\frac{28}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{84}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{-75x} +35 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{-84} \\\Leftrightarrow & -210x+75x& = & 35-84 \\\Leftrightarrow & \color{red}{-135} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-135} & & \\\Leftrightarrow & x = \frac{49}{135} & & \\ & V = \left\{ \frac{49}{135} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-80} & = & \color{red}{60x} +7 \\\Leftrightarrow & -144x \color{red}{-80} \color{blue}{+80} \color{blue}{-60x} & = & \color{red}{60x} +7 \color{blue}{-60x} \color{blue}{+80} \\\Leftrightarrow & -144x-60x& = & 7+80 \\\Leftrightarrow & \color{red}{-204} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-204} & & \\\Leftrightarrow & x = \frac{-29}{68} & & \\ & V = \left\{ \frac{-29}{68} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 18x-\frac{12}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{-12} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 126x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 126x+35x& = & 10+12 \\\Leftrightarrow & \color{red}{161} x& = & 22 \\\Leftrightarrow & x = \frac{22}{161} & & \\ & V = \left\{ \frac{22}{161} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-66} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 330x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 330x+385x& = & 10+66 \\\Leftrightarrow & \color{red}{715} x& = & 76 \\\Leftrightarrow & x = \frac{76}{715} & & \\ & V = \left\{ \frac{76}{715} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{9}{5}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+99} & = & \color{red}{-220x} +50 \\\Leftrightarrow & -825x \color{red}{+99} \color{blue}{-99} \color{blue}{+220x} & = & \color{red}{-220x} +50 \color{blue}{+220x} \color{blue}{-99} \\\Leftrightarrow & -825x+220x& = & 50-99 \\\Leftrightarrow & \color{red}{-605} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-605} & & \\\Leftrightarrow & x = \frac{49}{605} & & \\ & V = \left\{ \frac{49}{605} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+16} & = & \color{red}{154x} +33 \\\Leftrightarrow & 440x \color{red}{+16} \color{blue}{-16} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-16} \\\Leftrightarrow & 440x-154x& = & 33-16 \\\Leftrightarrow & \color{red}{286} x& = & 17 \\\Leftrightarrow & x = \frac{17}{286} & & \\ & V = \left\{ \frac{17}{286} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{7})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{175x} +14 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-175x} & = & \color{red}{175x} +14 \color{blue}{-175x} \color{blue}{+60} \\\Leftrightarrow & 420x-175x& = & 14+60 \\\Leftrightarrow & \color{red}{245} x& = & 74 \\\Leftrightarrow & x = \frac{74}{245} & & \\ & V = \left\{ \frac{74}{245} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{3})& = & 8x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{28}{3}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-140} & = & \color{red}{120x} +6 \\\Leftrightarrow & 315x \color{red}{-140} \color{blue}{+140} \color{blue}{-120x} & = & \color{red}{120x} +6 \color{blue}{-120x} \color{blue}{+140} \\\Leftrightarrow & 315x-120x& = & 6+140 \\\Leftrightarrow & \color{red}{195} x& = & 146 \\\Leftrightarrow & x = \frac{146}{195} & & \\ & V = \left\{ \frac{146}{195} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 16x-\frac{12}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-132} & = & \color{red}{385x} +56 \\\Leftrightarrow & 1232x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 1232x-385x& = & 56+132 \\\Leftrightarrow & \color{red}{847} x& = & 188 \\\Leftrightarrow & x = \frac{188}{847} & & \\ & V = \left\{ \frac{188}{847} \right\} & \\\end{align}\)
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