Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{3})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+140} & = & \color{red}{-120x} +12 \\\Leftrightarrow & -315x \color{red}{+140} \color{blue}{-140} \color{blue}{+120x} & = & \color{red}{-120x} +12 \color{blue}{+120x} \color{blue}{-140} \\\Leftrightarrow & -315x+120x& = & 12-140 \\\Leftrightarrow & \color{red}{-195} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-195} & & \\\Leftrightarrow & x = \frac{128}{195} & & \\ & V = \left\{ \frac{128}{195} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+9} & = & \color{red}{25x} +7 \\\Leftrightarrow & 60x \color{red}{+9} \color{blue}{-9} \color{blue}{-25x} & = & \color{red}{25x} +7 \color{blue}{-25x} \color{blue}{-9} \\\Leftrightarrow & 60x-25x& = & 7-9 \\\Leftrightarrow & \color{red}{35} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{6}{5}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-42} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -280x \color{red}{-42} \color{blue}{+42} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+42} \\\Leftrightarrow & -280x+315x& = & 20+42 \\\Leftrightarrow & \color{red}{35} x& = & 62 \\\Leftrightarrow & x = \frac{62}{35} & & \\ & V = \left\{ \frac{62}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{231x} +21 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{-66} \\\Leftrightarrow & 616x-231x& = & 21-66 \\\Leftrightarrow & \color{red}{385} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{385} & & \\\Leftrightarrow & x = \frac{-9}{77} & & \\ & V = \left\{ \frac{-9}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+84} & = & \color{red}{245x} +25 \\\Leftrightarrow & -840x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -840x-245x& = & 25-84 \\\Leftrightarrow & \color{red}{-1085} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-1085} & & \\\Leftrightarrow & x = \frac{59}{1085} & & \\ & V = \left\{ \frac{59}{1085} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{10}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{165x} +44 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+30} \\\Leftrightarrow & -132x-165x& = & 44+30 \\\Leftrightarrow & \color{red}{-297} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-297} & & \\\Leftrightarrow & x = \frac{-74}{297} & & \\ & V = \left\{ \frac{-74}{297} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{5})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -14x-\frac{28}{5}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x- \frac{56}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{-56} & = & \color{red}{-30x} +3 \\\Leftrightarrow & -140x \color{red}{-56} \color{blue}{+56} \color{blue}{+30x} & = & \color{red}{-30x} +3 \color{blue}{+30x} \color{blue}{+56} \\\Leftrightarrow & -140x+30x& = & 3+56 \\\Leftrightarrow & \color{red}{-110} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-110} & & \\\Leftrightarrow & x = \frac{-59}{110} & & \\ & V = \left\{ \frac{-59}{110} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & -420x+98x& = & 35+60 \\\Leftrightarrow & \color{red}{-322} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-322} & & \\\Leftrightarrow & x = \frac{-95}{322} & & \\ & V = \left\{ \frac{-95}{322} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+28} & = & \color{red}{-18x} +9 \\\Leftrightarrow & 84x \color{red}{+28} \color{blue}{-28} \color{blue}{+18x} & = & \color{red}{-18x} +9 \color{blue}{+18x} \color{blue}{-28} \\\Leftrightarrow & 84x+18x& = & 9-28 \\\Leftrightarrow & \color{red}{102} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{102} & & \\ & V = \left\{ \frac{-19}{102} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{24}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+24} \\\Leftrightarrow & -120x+35x& = & 6+24 \\\Leftrightarrow & \color{red}{-85} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-85} & & \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -28x-\frac{35}{3}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-175} & = & \color{red}{75x} +21 \\\Leftrightarrow & -420x \color{red}{-175} \color{blue}{+175} \color{blue}{-75x} & = & \color{red}{75x} +21 \color{blue}{-75x} \color{blue}{+175} \\\Leftrightarrow & -420x-75x& = & 21+175 \\\Leftrightarrow & \color{red}{-495} x& = & 196 \\\Leftrightarrow & x = \frac{196}{-495} & & \\\Leftrightarrow & x = \frac{-196}{495} & & \\ & V = \left\{ \frac{-196}{495} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 70+110 \\\Leftrightarrow & \color{red}{-231} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-231} & & \\\Leftrightarrow & x = \frac{-60}{77} & & \\ & V = \left\{ \frac{-60}{77} \right\} & \\\end{align}\)
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