Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{11})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{8}{11}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-24} \\\Leftrightarrow & -132x+297x& = & 88-24 \\\Leftrightarrow & \color{red}{165} x& = & 64 \\\Leftrightarrow & x = \frac{64}{165} & & \\ & V = \left\{ \frac{64}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & 594x+165x& = & 22+54 \\\Leftrightarrow & \color{red}{759} x& = & 76 \\\Leftrightarrow & x = \frac{76}{759} & & \\ & V = \left\{ \frac{76}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+10} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 90x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & 90x+63x& = & 6-10 \\\Leftrightarrow & \color{red}{153} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{153} & & \\ & V = \left\{ \frac{-4}{153} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{10})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 35x+\frac{21}{10}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+21} & = & \color{red}{-20x} +18 \\\Leftrightarrow & 350x \color{red}{+21} \color{blue}{-21} \color{blue}{+20x} & = & \color{red}{-20x} +18 \color{blue}{+20x} \color{blue}{-21} \\\Leftrightarrow & 350x+20x& = & 18-21 \\\Leftrightarrow & \color{red}{370} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{370} & & \\ & V = \left\{ \frac{-3}{370} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3300}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3300x \color{red}{+180} & = & \color{red}{770x} +33 \\\Leftrightarrow & 3300x \color{red}{+180} \color{blue}{-180} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{-180} \\\Leftrightarrow & 3300x-770x& = & 33-180 \\\Leftrightarrow & \color{red}{2530} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{2530} & & \\ & V = \left\{ \frac{-147}{2530} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{5})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -21x-\frac{28}{5}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{-120x} +50 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{+120x} & = & \color{red}{-120x} +50 \color{blue}{+120x} \color{blue}{+84} \\\Leftrightarrow & -315x+120x& = & 50+84 \\\Leftrightarrow & \color{red}{-195} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-195} & & \\\Leftrightarrow & x = \frac{-134}{195} & & \\ & V = \left\{ \frac{-134}{195} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{+20} & = & \color{red}{198x} +77 \\\Leftrightarrow & -88x \color{red}{+20} \color{blue}{-20} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{-20} \\\Leftrightarrow & -88x-198x& = & 77-20 \\\Leftrightarrow & \color{red}{-286} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-286} & & \\\Leftrightarrow & x = \frac{-57}{286} & & \\ & V = \left\{ \frac{-57}{286} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-10} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -90x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -90x+63x& = & 6+10 \\\Leftrightarrow & \color{red}{-27} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-27} & & \\\Leftrightarrow & x = \frac{-16}{27} & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-30} \\\Leftrightarrow & 330x+231x& = & 110-30 \\\Leftrightarrow & \color{red}{561} x& = & 80 \\\Leftrightarrow & x = \frac{80}{561} & & \\ & V = \left\{ \frac{80}{561} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+54} & = & \color{red}{165x} +88 \\\Leftrightarrow & 792x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & 792x-165x& = & 88-54 \\\Leftrightarrow & \color{red}{627} x& = & 34 \\\Leftrightarrow & x = \frac{34}{627} & & \\ & V = \left\{ \frac{34}{627} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{7})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 9x+\frac{12}{7}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{+108} & = & \color{red}{252x} +70 \\\Leftrightarrow & 567x \color{red}{+108} \color{blue}{-108} \color{blue}{-252x} & = & \color{red}{252x} +70 \color{blue}{-252x} \color{blue}{-108} \\\Leftrightarrow & 567x-252x& = & 70-108 \\\Leftrightarrow & \color{red}{315} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{315} & & \\ & V = \left\{ \frac{-38}{315} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{11})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2112}{ \color{blue}{88} }x- \frac{240}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2112x \color{red}{-240} & = & \color{red}{440x} +55 \\\Leftrightarrow & 2112x \color{red}{-240} \color{blue}{+240} \color{blue}{-440x} & = & \color{red}{440x} +55 \color{blue}{-440x} \color{blue}{+240} \\\Leftrightarrow & 2112x-440x& = & 55+240 \\\Leftrightarrow & \color{red}{1672} x& = & 295 \\\Leftrightarrow & x = \frac{295}{1672} & & \\ & V = \left\{ \frac{295}{1672} \right\} & \\\end{align}\)
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