Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{5})& = & -4x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+99} & = & \color{red}{-220x} +35 \\\Leftrightarrow & 825x \color{red}{+99} \color{blue}{-99} \color{blue}{+220x} & = & \color{red}{-220x} +35 \color{blue}{+220x} \color{blue}{-99} \\\Leftrightarrow & 825x+220x& = & 35-99 \\\Leftrightarrow & \color{red}{1045} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{1045} & & \\ & V = \left\{ \frac{-64}{1045} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{21x} +8 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & -60x-21x& = & 8-20 \\\Leftrightarrow & \color{red}{-81} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-81} & & \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{7})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-12} & = & \color{red}{-56x} +49 \\\Leftrightarrow & 210x \color{red}{-12} \color{blue}{+12} \color{blue}{+56x} & = & \color{red}{-56x} +49 \color{blue}{+56x} \color{blue}{+12} \\\Leftrightarrow & 210x+56x& = & 49+12 \\\Leftrightarrow & \color{red}{266} x& = & 61 \\\Leftrightarrow & x = \frac{61}{266} & & \\ & V = \left\{ \frac{61}{266} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{21}{11}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-63} & = & \color{red}{66x} +22 \\\Leftrightarrow & 1155x \color{red}{-63} \color{blue}{+63} \color{blue}{-66x} & = & \color{red}{66x} +22 \color{blue}{-66x} \color{blue}{+63} \\\Leftrightarrow & 1155x-66x& = & 22+63 \\\Leftrightarrow & \color{red}{1089} x& = & 85 \\\Leftrightarrow & x = \frac{85}{1089} & & \\ & V = \left\{ \frac{85}{1089} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -20x+\frac{15}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1400}{ \color{blue}{70} }x+ \frac{150}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1400x \color{red}{+150} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -1400x \color{red}{+150} \color{blue}{-150} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{-150} \\\Leftrightarrow & -1400x+490x& = & 49-150 \\\Leftrightarrow & \color{red}{-910} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{-910} & & \\\Leftrightarrow & x = \frac{101}{910} & & \\ & V = \left\{ \frac{101}{910} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{7})& = & -4x+\frac{5}{2} \\\Leftrightarrow & -15x+\frac{15}{7}& = & -4x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-56x} +35 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+56x} & = & \color{red}{-56x} +35 \color{blue}{+56x} \color{blue}{-30} \\\Leftrightarrow & -210x+56x& = & 35-30 \\\Leftrightarrow & \color{red}{-154} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-154} & & \\\Leftrightarrow & x = \frac{-5}{154} & & \\ & V = \left\{ \frac{-5}{154} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{15}{7}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+15} & = & \color{red}{-63x} +10 \\\Leftrightarrow & 140x \color{red}{+15} \color{blue}{-15} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-15} \\\Leftrightarrow & 140x+63x& = & 10-15 \\\Leftrightarrow & \color{red}{203} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{203} & & \\ & V = \left\{ \frac{-5}{203} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 120x+25x& = & 4-24 \\\Leftrightarrow & \color{red}{145} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{145} & & \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{1}{3})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{7}{3}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+7} & = & \color{red}{24x} +2 \\\Leftrightarrow & -63x \color{red}{+7} \color{blue}{-7} \color{blue}{-24x} & = & \color{red}{24x} +2 \color{blue}{-24x} \color{blue}{-7} \\\Leftrightarrow & -63x-24x& = & 2-7 \\\Leftrightarrow & \color{red}{-87} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-87} & & \\\Leftrightarrow & x = \frac{5}{87} & & \\ & V = \left\{ \frac{5}{87} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{3})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -10x-\frac{10}{3}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x- \frac{100}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{-100} & = & \color{red}{210x} +9 \\\Leftrightarrow & -300x \color{red}{-100} \color{blue}{+100} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{+100} \\\Leftrightarrow & -300x-210x& = & 9+100 \\\Leftrightarrow & \color{red}{-510} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-510} & & \\\Leftrightarrow & x = \frac{-109}{510} & & \\ & V = \left\{ \frac{-109}{510} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+32} & = & \color{red}{360x} +15 \\\Leftrightarrow & -320x \color{red}{+32} \color{blue}{-32} \color{blue}{-360x} & = & \color{red}{360x} +15 \color{blue}{-360x} \color{blue}{-32} \\\Leftrightarrow & -320x-360x& = & 15-32 \\\Leftrightarrow & \color{red}{-680} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-680} & & \\\Leftrightarrow & x = \frac{1}{40} & & \\ & V = \left\{ \frac{1}{40} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -25x+\frac{25}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x+ \frac{225}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{+225} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -2475x \color{red}{+225} \color{blue}{-225} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{-225} \\\Leftrightarrow & -2475x+693x& = & 88-225 \\\Leftrightarrow & \color{red}{-1782} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-1782} & & \\\Leftrightarrow & x = \frac{137}{1782} & & \\ & V = \left\{ \frac{137}{1782} \right\} & \\\end{align}\)
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