Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{4}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{36}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-36} & = & \color{red}{495x} +22 \\\Leftrightarrow & 792x \color{red}{-36} \color{blue}{+36} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{+36} \\\Leftrightarrow & 792x-495x& = & 22+36 \\\Leftrightarrow & \color{red}{297} x& = & 58 \\\Leftrightarrow & x = \frac{58}{297} & & \\ & V = \left\{ \frac{58}{297} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{4})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{-96x} +40 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +40 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & -180x+96x& = & 40+45 \\\Leftrightarrow & \color{red}{-84} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-84} & & \\\Leftrightarrow & x = \frac{-85}{84} & & \\ & V = \left\{ \frac{-85}{84} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+264} & = & \color{red}{-275x} +45 \\\Leftrightarrow & 1320x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 1320x+275x& = & 45-264 \\\Leftrightarrow & \color{red}{1595} x& = & -219 \\\Leftrightarrow & x = \frac{-219}{1595} & & \\ & V = \left\{ \frac{-219}{1595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -924x+385x& = & 33-126 \\\Leftrightarrow & \color{red}{-539} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-539} & & \\\Leftrightarrow & x = \frac{93}{539} & & \\ & V = \left\{ \frac{93}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & 8x+\frac{3}{4} \\\Leftrightarrow & 21x+\frac{28}{9}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{756}{ \color{blue}{36} }x+ \frac{112}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 756x \color{red}{+112} & = & \color{red}{288x} +27 \\\Leftrightarrow & 756x \color{red}{+112} \color{blue}{-112} \color{blue}{-288x} & = & \color{red}{288x} +27 \color{blue}{-288x} \color{blue}{-112} \\\Leftrightarrow & 756x-288x& = & 27-112 \\\Leftrightarrow & \color{red}{468} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{468} & & \\ & V = \left\{ \frac{-85}{468} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{-99x} +15 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{+99x} & = & \color{red}{-99x} +15 \color{blue}{+99x} \color{blue}{-220} \\\Leftrightarrow & 660x+99x& = & 15-220 \\\Leftrightarrow & \color{red}{759} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{759} & & \\ & V = \left\{ \frac{-205}{759} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-20} & = & \color{red}{70x} +49 \\\Leftrightarrow & 84x \color{red}{-20} \color{blue}{+20} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{+20} \\\Leftrightarrow & 84x-70x& = & 49+20 \\\Leftrightarrow & \color{red}{14} x& = & 69 \\\Leftrightarrow & x = \frac{69}{14} & & \\ & V = \left\{ \frac{69}{14} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{5})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 20x-\frac{16}{5}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x- \frac{128}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{-128} & = & \color{red}{-280x} +15 \\\Leftrightarrow & 800x \color{red}{-128} \color{blue}{+128} \color{blue}{+280x} & = & \color{red}{-280x} +15 \color{blue}{+280x} \color{blue}{+128} \\\Leftrightarrow & 800x+280x& = & 15+128 \\\Leftrightarrow & \color{red}{1080} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1080} & & \\ & V = \left\{ \frac{143}{1080} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{8}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+16} & = & \color{red}{154x} +33 \\\Leftrightarrow & 176x \color{red}{+16} \color{blue}{-16} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-16} \\\Leftrightarrow & 176x-154x& = & 33-16 \\\Leftrightarrow & \color{red}{22} x& = & 17 \\\Leftrightarrow & x = \frac{17}{22} & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+72} & = & \color{red}{231x} +22 \\\Leftrightarrow & 990x \color{red}{+72} \color{blue}{-72} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-72} \\\Leftrightarrow & 990x-231x& = & 22-72 \\\Leftrightarrow & \color{red}{759} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{759} & & \\ & V = \left\{ \frac{-50}{759} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{20}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+60} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -336x \color{red}{+60} \color{blue}{-60} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-60} \\\Leftrightarrow & -336x+147x& = & 70-60 \\\Leftrightarrow & \color{red}{-189} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-189} & & \\\Leftrightarrow & x = \frac{-10}{189} & & \\ & V = \left\{ \frac{-10}{189} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{8})& = & 2x+\frac{10}{11} \\\Leftrightarrow & -25x-\frac{25}{8}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{-275} & = & \color{red}{176x} +80 \\\Leftrightarrow & -2200x \color{red}{-275} \color{blue}{+275} \color{blue}{-176x} & = & \color{red}{176x} +80 \color{blue}{-176x} \color{blue}{+275} \\\Leftrightarrow & -2200x-176x& = & 80+275 \\\Leftrightarrow & \color{red}{-2376} x& = & 355 \\\Leftrightarrow & x = \frac{355}{-2376} & & \\\Leftrightarrow & x = \frac{-355}{2376} & & \\ & V = \left\{ \frac{-355}{2376} \right\} & \\\end{align}\)
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