Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{-25x} +3 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +3 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 60x+25x& = & 3-24 \\\Leftrightarrow & \color{red}{85} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{85} & & \\ & V = \left\{ \frac{-21}{85} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{-98} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -980x \color{red}{-98} \color{blue}{+98} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+98} \\\Leftrightarrow & -980x+315x& = & 50+98 \\\Leftrightarrow & \color{red}{-665} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-665} & & \\\Leftrightarrow & x = \frac{-148}{665} & & \\ & V = \left\{ \frac{-148}{665} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+110} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -132x \color{red}{+110} \color{blue}{-110} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-110} \\\Leftrightarrow & -132x+297x& = & 18-110 \\\Leftrightarrow & \color{red}{165} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{165} & & \\ & V = \left\{ \frac{-92}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-32} & = & \color{red}{84x} +9 \\\Leftrightarrow & 120x \color{red}{-32} \color{blue}{+32} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{+32} \\\Leftrightarrow & 120x-84x& = & 9+32 \\\Leftrightarrow & \color{red}{36} x& = & 41 \\\Leftrightarrow & x = \frac{41}{36} & & \\ & V = \left\{ \frac{41}{36} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -30x-\frac{12}{11}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-12} & = & \color{red}{-77x} +3 \\\Leftrightarrow & -330x \color{red}{-12} \color{blue}{+12} \color{blue}{+77x} & = & \color{red}{-77x} +3 \color{blue}{+77x} \color{blue}{+12} \\\Leftrightarrow & -330x+77x& = & 3+12 \\\Leftrightarrow & \color{red}{-253} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-253} & & \\\Leftrightarrow & x = \frac{-15}{253} & & \\ & V = \left\{ \frac{-15}{253} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{-539x} +14 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+330} \\\Leftrightarrow & 1848x+539x& = & 14+330 \\\Leftrightarrow & \color{red}{2387} x& = & 344 \\\Leftrightarrow & x = \frac{344}{2387} & & \\ & V = \left\{ \frac{344}{2387} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x- \frac{32}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{-32} & = & \color{red}{280x} +35 \\\Leftrightarrow & -240x \color{red}{-32} \color{blue}{+32} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+32} \\\Leftrightarrow & -240x-280x& = & 35+32 \\\Leftrightarrow & \color{red}{-520} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-520} & & \\\Leftrightarrow & x = \frac{-67}{520} & & \\ & V = \left\{ \frac{-67}{520} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{16}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+32} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -168x \color{red}{+32} \color{blue}{-32} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-32} \\\Leftrightarrow & -168x+70x& = & 63-32 \\\Leftrightarrow & \color{red}{-98} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-98} & & \\\Leftrightarrow & x = \frac{-31}{98} & & \\ & V = \left\{ \frac{-31}{98} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{11})& = & -6x+\frac{10}{3} \\\Leftrightarrow & -35x+\frac{14}{11}& = & -6x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{42}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+42} & = & \color{red}{-198x} +110 \\\Leftrightarrow & -1155x \color{red}{+42} \color{blue}{-42} \color{blue}{+198x} & = & \color{red}{-198x} +110 \color{blue}{+198x} \color{blue}{-42} \\\Leftrightarrow & -1155x+198x& = & 110-42 \\\Leftrightarrow & \color{red}{-957} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-957} & & \\\Leftrightarrow & x = \frac{-68}{957} & & \\ & V = \left\{ \frac{-68}{957} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 10x+\frac{15}{2}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+75} & = & \color{red}{30x} +3 \\\Leftrightarrow & 100x \color{red}{+75} \color{blue}{-75} \color{blue}{-30x} & = & \color{red}{30x} +3 \color{blue}{-30x} \color{blue}{-75} \\\Leftrightarrow & 100x-30x& = & 3-75 \\\Leftrightarrow & \color{red}{70} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{70} & & \\\Leftrightarrow & x = \frac{-36}{35} & & \\ & V = \left\{ \frac{-36}{35} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{9})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{20}{9}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{-162x} +15 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{+162x} & = & \color{red}{-162x} +15 \color{blue}{+162x} \color{blue}{-40} \\\Leftrightarrow & 360x+162x& = & 15-40 \\\Leftrightarrow & \color{red}{522} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{522} & & \\ & V = \left\{ \frac{-25}{522} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{245x} +42 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-30} \\\Leftrightarrow & -210x-245x& = & 42-30 \\\Leftrightarrow & \color{red}{-455} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-455} & & \\\Leftrightarrow & x = \frac{-12}{455} & & \\ & V = \left\{ \frac{-12}{455} \right\} & \\\end{align}\)
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