Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{12})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{35}{12}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{-35} & = & \color{red}{36x} +16 \\\Leftrightarrow & 168x \color{red}{-35} \color{blue}{+35} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{+35} \\\Leftrightarrow & 168x-36x& = & 16+35 \\\Leftrightarrow & \color{red}{132} x& = & 51 \\\Leftrightarrow & x = \frac{51}{132} & & \\\Leftrightarrow & x = \frac{17}{44} & & \\ & V = \left\{ \frac{17}{44} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{4})& = & -8x+\frac{10}{11} \\\Leftrightarrow & -28x+\frac{35}{4}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{385}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+385} & = & \color{red}{-352x} +40 \\\Leftrightarrow & -1232x \color{red}{+385} \color{blue}{-385} \color{blue}{+352x} & = & \color{red}{-352x} +40 \color{blue}{+352x} \color{blue}{-385} \\\Leftrightarrow & -1232x+352x& = & 40-385 \\\Leftrightarrow & \color{red}{-880} x& = & -345 \\\Leftrightarrow & x = \frac{-345}{-880} & & \\\Leftrightarrow & x = \frac{69}{176} & & \\ & V = \left\{ \frac{69}{176} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & 9x+\frac{7}{12} \\\Leftrightarrow & -35x-\frac{14}{11}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-4620}{ \color{blue}{132} }x- \frac{168}{ \color{blue}{132} })& = & (\frac{1188}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -4620x \color{red}{-168} & = & \color{red}{1188x} +77 \\\Leftrightarrow & -4620x \color{red}{-168} \color{blue}{+168} \color{blue}{-1188x} & = & \color{red}{1188x} +77 \color{blue}{-1188x} \color{blue}{+168} \\\Leftrightarrow & -4620x-1188x& = & 77+168 \\\Leftrightarrow & \color{red}{-5808} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-5808} & & \\\Leftrightarrow & x = \frac{-245}{5808} & & \\ & V = \left\{ \frac{-245}{5808} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{-80} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -560x \color{red}{-80} \color{blue}{+80} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{+80} \\\Leftrightarrow & -560x+245x& = & 14+80 \\\Leftrightarrow & \color{red}{-315} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-315} & & \\\Leftrightarrow & x = \frac{-94}{315} & & \\ & V = \left\{ \frac{-94}{315} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -16x+\frac{8}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+72} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -1584x \color{red}{+72} \color{blue}{-72} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{-72} \\\Leftrightarrow & -1584x+693x& = & 88-72 \\\Leftrightarrow & \color{red}{-891} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-891} & & \\\Leftrightarrow & x = \frac{-16}{891} & & \\ & V = \left\{ \frac{-16}{891} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{6})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{35}{6}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{-175} & = & \color{red}{240x} +48 \\\Leftrightarrow & -630x \color{red}{-175} \color{blue}{+175} \color{blue}{-240x} & = & \color{red}{240x} +48 \color{blue}{-240x} \color{blue}{+175} \\\Leftrightarrow & -630x-240x& = & 48+175 \\\Leftrightarrow & \color{red}{-870} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-870} & & \\\Leftrightarrow & x = \frac{-223}{870} & & \\ & V = \left\{ \frac{-223}{870} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+220} & = & \color{red}{-297x} +6 \\\Leftrightarrow & -825x \color{red}{+220} \color{blue}{-220} \color{blue}{+297x} & = & \color{red}{-297x} +6 \color{blue}{+297x} \color{blue}{-220} \\\Leftrightarrow & -825x+297x& = & 6-220 \\\Leftrightarrow & \color{red}{-528} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-528} & & \\\Leftrightarrow & x = \frac{107}{264} & & \\ & V = \left\{ \frac{107}{264} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -10x-\frac{6}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-54} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -450x \color{red}{-54} \color{blue}{+54} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+54} \\\Leftrightarrow & -450x+315x& = & 50+54 \\\Leftrightarrow & \color{red}{-135} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-135} & & \\\Leftrightarrow & x = \frac{-104}{135} & & \\ & V = \left\{ \frac{-104}{135} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{-162} & = & \color{red}{693x} +55 \\\Leftrightarrow & 2970x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & 2970x-693x& = & 55+162 \\\Leftrightarrow & \color{red}{2277} x& = & 217 \\\Leftrightarrow & x = \frac{217}{2277} & & \\ & V = \left\{ \frac{217}{2277} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{147x} +35 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{-60} \\\Leftrightarrow & 336x-147x& = & 35-60 \\\Leftrightarrow & \color{red}{189} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{189} & & \\ & V = \left\{ \frac{-25}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{9})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 35x+\frac{28}{9}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{630}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 630x \color{red}{+56} & = & \color{red}{144x} +81 \\\Leftrightarrow & 630x \color{red}{+56} \color{blue}{-56} \color{blue}{-144x} & = & \color{red}{144x} +81 \color{blue}{-144x} \color{blue}{-56} \\\Leftrightarrow & 630x-144x& = & 81-56 \\\Leftrightarrow & \color{red}{486} x& = & 25 \\\Leftrightarrow & x = \frac{25}{486} & & \\ & V = \left\{ \frac{25}{486} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{4}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{21x} +4 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+4} \\\Leftrightarrow & -30x-21x& = & 4+4 \\\Leftrightarrow & \color{red}{-51} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-51} & & \\\Leftrightarrow & x = \frac{-8}{51} & & \\ & V = \left\{ \frac{-8}{51} \right\} & \\\end{align}\)
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