Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{24x} +40 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{-24x} & = & \color{red}{24x} +40 \color{blue}{-24x} \color{blue}{+45} \\\Leftrightarrow & 180x-24x& = & 40+45 \\\Leftrightarrow & \color{red}{156} x& = & 85 \\\Leftrightarrow & x = \frac{85}{156} & & \\ & V = \left\{ \frac{85}{156} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+154} & = & \color{red}{-264x} +12 \\\Leftrightarrow & -693x \color{red}{+154} \color{blue}{-154} \color{blue}{+264x} & = & \color{red}{-264x} +12 \color{blue}{+264x} \color{blue}{-154} \\\Leftrightarrow & -693x+264x& = & 12-154 \\\Leftrightarrow & \color{red}{-429} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{-429} & & \\\Leftrightarrow & x = \frac{142}{429} & & \\ & V = \left\{ \frac{142}{429} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & -9x+\frac{9}{8} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+112} & = & \color{red}{-216x} +27 \\\Leftrightarrow & 672x \color{red}{+112} \color{blue}{-112} \color{blue}{+216x} & = & \color{red}{-216x} +27 \color{blue}{+216x} \color{blue}{-112} \\\Leftrightarrow & 672x+216x& = & 27-112 \\\Leftrightarrow & \color{red}{888} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{888} & & \\ & V = \left\{ \frac{-85}{888} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-60} & = & \color{red}{105x} +35 \\\Leftrightarrow & -252x \color{red}{-60} \color{blue}{+60} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{+60} \\\Leftrightarrow & -252x-105x& = & 35+60 \\\Leftrightarrow & \color{red}{-357} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-357} & & \\\Leftrightarrow & x = \frac{-95}{357} & & \\ & V = \left\{ \frac{-95}{357} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{8})& = & -8x+\frac{2}{7} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -8x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1568x \color{red}{+147} & = & \color{red}{-448x} +16 \\\Leftrightarrow & -1568x \color{red}{+147} \color{blue}{-147} \color{blue}{+448x} & = & \color{red}{-448x} +16 \color{blue}{+448x} \color{blue}{-147} \\\Leftrightarrow & -1568x+448x& = & 16-147 \\\Leftrightarrow & \color{red}{-1120} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-1120} & & \\\Leftrightarrow & x = \frac{131}{1120} & & \\ & V = \left\{ \frac{131}{1120} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{3})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{10}{3}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{40}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{84x} +5 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{-84x} & = & \color{red}{84x} +5 \color{blue}{-84x} \color{blue}{+40} \\\Leftrightarrow & 120x-84x& = & 5+40 \\\Leftrightarrow & \color{red}{36} x& = & 45 \\\Leftrightarrow & x = \frac{45}{36} & & \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{8}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1120}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1120x \color{red}{-80} & = & \color{red}{490x} +63 \\\Leftrightarrow & -1120x \color{red}{-80} \color{blue}{+80} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+80} \\\Leftrightarrow & -1120x-490x& = & 63+80 \\\Leftrightarrow & \color{red}{-1610} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1610} & & \\\Leftrightarrow & x = \frac{-143}{1610} & & \\ & V = \left\{ \frac{-143}{1610} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{20}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{75}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 75x \color{red}{+20} & = & \color{red}{9x} +4 \\\Leftrightarrow & 75x \color{red}{+20} \color{blue}{-20} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{-20} \\\Leftrightarrow & 75x-9x& = & 4-20 \\\Leftrightarrow & \color{red}{66} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{66} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{11})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{25}{11}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-25} & = & \color{red}{99x} +6 \\\Leftrightarrow & 220x \color{red}{-25} \color{blue}{+25} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{+25} \\\Leftrightarrow & 220x-99x& = & 6+25 \\\Leftrightarrow & \color{red}{121} x& = & 31 \\\Leftrightarrow & x = \frac{31}{121} & & \\ & V = \left\{ \frac{31}{121} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-60} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -880x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & -880x+385x& = & 44+60 \\\Leftrightarrow & \color{red}{-495} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-495} & & \\\Leftrightarrow & x = \frac{-104}{495} & & \\ & V = \left\{ \frac{-104}{495} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -20x+\frac{10}{3}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+50} & = & \color{red}{135x} +12 \\\Leftrightarrow & -300x \color{red}{+50} \color{blue}{-50} \color{blue}{-135x} & = & \color{red}{135x} +12 \color{blue}{-135x} \color{blue}{-50} \\\Leftrightarrow & -300x-135x& = & 12-50 \\\Leftrightarrow & \color{red}{-435} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-435} & & \\\Leftrightarrow & x = \frac{38}{435} & & \\ & V = \left\{ \frac{38}{435} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & -4x+\frac{3}{11} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -4x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-220} & = & \color{red}{-132x} +9 \\\Leftrightarrow & -495x \color{red}{-220} \color{blue}{+220} \color{blue}{+132x} & = & \color{red}{-132x} +9 \color{blue}{+132x} \color{blue}{+220} \\\Leftrightarrow & -495x+132x& = & 9+220 \\\Leftrightarrow & \color{red}{-363} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-363} & & \\\Leftrightarrow & x = \frac{-229}{363} & & \\ & V = \left\{ \frac{-229}{363} \right\} & \\\end{align}\)
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