Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-54} & = & \color{red}{-165x} +77 \\\Leftrightarrow & 396x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +77 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & 396x+165x& = & 77+54 \\\Leftrightarrow & \color{red}{561} x& = & 131 \\\Leftrightarrow & x = \frac{131}{561} & & \\ & V = \left\{ \frac{131}{561} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 15x+\frac{9}{10}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+9} & = & \color{red}{-70x} +16 \\\Leftrightarrow & 150x \color{red}{+9} \color{blue}{-9} \color{blue}{+70x} & = & \color{red}{-70x} +16 \color{blue}{+70x} \color{blue}{-9} \\\Leftrightarrow & 150x+70x& = & 16-9 \\\Leftrightarrow & \color{red}{220} x& = & 7 \\\Leftrightarrow & x = \frac{7}{220} & & \\ & V = \left\{ \frac{7}{220} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{9})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 16x-\frac{20}{9}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-220} & = & \color{red}{297x} +72 \\\Leftrightarrow & 1584x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +72 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 1584x-297x& = & 72+220 \\\Leftrightarrow & \color{red}{1287} x& = & 292 \\\Leftrightarrow & x = \frac{292}{1287} & & \\ & V = \left\{ \frac{292}{1287} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 630x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{805} x& = & 99 \\\Leftrightarrow & x = \frac{99}{805} & & \\ & V = \left\{ \frac{99}{805} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{9})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{72}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 72x \color{red}{+8} & = & \color{red}{-90x} +63 \\\Leftrightarrow & 72x \color{red}{+8} \color{blue}{-8} \color{blue}{+90x} & = & \color{red}{-90x} +63 \color{blue}{+90x} \color{blue}{-8} \\\Leftrightarrow & 72x+90x& = & 63-8 \\\Leftrightarrow & \color{red}{162} x& = & 55 \\\Leftrightarrow & x = \frac{55}{162} & & \\ & V = \left\{ \frac{55}{162} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{9})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{20}{9}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-20} & = & \color{red}{81x} +24 \\\Leftrightarrow & -72x \color{red}{-20} \color{blue}{+20} \color{blue}{-81x} & = & \color{red}{81x} +24 \color{blue}{-81x} \color{blue}{+20} \\\Leftrightarrow & -72x-81x& = & 24+20 \\\Leftrightarrow & \color{red}{-153} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-153} & & \\\Leftrightarrow & x = \frac{-44}{153} & & \\ & V = \left\{ \frac{-44}{153} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{4})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x-\frac{21}{4}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-280}{ \color{blue}{20} }x- \frac{105}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{-60x} +32 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{+60x} & = & \color{red}{-60x} +32 \color{blue}{+60x} \color{blue}{+105} \\\Leftrightarrow & -280x+60x& = & 32+105 \\\Leftrightarrow & \color{red}{-220} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-220} & & \\\Leftrightarrow & x = \frac{-137}{220} & & \\ & V = \left\{ \frac{-137}{220} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{+80} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 144x \color{red}{+80} \color{blue}{-80} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{-80} \\\Leftrightarrow & 144x+60x& = & 27-80 \\\Leftrightarrow & \color{red}{204} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{204} & & \\ & V = \left\{ \frac{-53}{204} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+90} & = & \color{red}{441x} +70 \\\Leftrightarrow & 504x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & 504x-441x& = & 70-90 \\\Leftrightarrow & \color{red}{63} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-288}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -288x \color{red}{-64} & = & \color{red}{-648x} +63 \\\Leftrightarrow & -288x \color{red}{-64} \color{blue}{+64} \color{blue}{+648x} & = & \color{red}{-648x} +63 \color{blue}{+648x} \color{blue}{+64} \\\Leftrightarrow & -288x+648x& = & 63+64 \\\Leftrightarrow & \color{red}{360} x& = & 127 \\\Leftrightarrow & x = \frac{127}{360} & & \\ & V = \left\{ \frac{127}{360} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{10}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+50} & = & \color{red}{45x} +18 \\\Leftrightarrow & -120x \color{red}{+50} \color{blue}{-50} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{-50} \\\Leftrightarrow & -120x-45x& = & 18-50 \\\Leftrightarrow & \color{red}{-165} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-165} & & \\\Leftrightarrow & x = \frac{32}{165} & & \\ & V = \left\{ \frac{32}{165} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-54} & = & \color{red}{441x} +14 \\\Leftrightarrow & -378x \color{red}{-54} \color{blue}{+54} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{+54} \\\Leftrightarrow & -378x-441x& = & 14+54 \\\Leftrightarrow & \color{red}{-819} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-819} & & \\\Leftrightarrow & x = \frac{-68}{819} & & \\ & V = \left\{ \frac{-68}{819} \right\} & \\\end{align}\)
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