Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{16}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+144} & = & \color{red}{495x} +110 \\\Leftrightarrow & 1188x \color{red}{+144} \color{blue}{-144} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{-144} \\\Leftrightarrow & 1188x-495x& = & 110-144 \\\Leftrightarrow & \color{red}{693} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{693} & & \\ & V = \left\{ \frac{-34}{693} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 9x+\frac{5}{7} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 9x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{-98} & = & \color{red}{189x} +15 \\\Leftrightarrow & -735x \color{red}{-98} \color{blue}{+98} \color{blue}{-189x} & = & \color{red}{189x} +15 \color{blue}{-189x} \color{blue}{+98} \\\Leftrightarrow & -735x-189x& = & 15+98 \\\Leftrightarrow & \color{red}{-924} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-924} & & \\\Leftrightarrow & x = \frac{-113}{924} & & \\ & V = \left\{ \frac{-113}{924} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-6} & = & \color{red}{-49x} +6 \\\Leftrightarrow & 70x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & 70x+49x& = & 6+6 \\\Leftrightarrow & \color{red}{119} x& = & 12 \\\Leftrightarrow & x = \frac{12}{119} & & \\ & V = \left\{ \frac{12}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{165x} +88 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -792x-165x& = & 88+54 \\\Leftrightarrow & \color{red}{-957} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-957} & & \\\Leftrightarrow & x = \frac{-142}{957} & & \\ & V = \left\{ \frac{-142}{957} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+24} & = & \color{red}{-110x} +77 \\\Leftrightarrow & 528x \color{red}{+24} \color{blue}{-24} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{-24} \\\Leftrightarrow & 528x+110x& = & 77-24 \\\Leftrightarrow & \color{red}{638} x& = & 53 \\\Leftrightarrow & x = \frac{53}{638} & & \\ & V = \left\{ \frac{53}{638} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{1}{2})& = & 8x+\frac{7}{9} \\\Leftrightarrow & -15x+\frac{5}{2}& = & 8x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{+45} & = & \color{red}{144x} +14 \\\Leftrightarrow & -270x \color{red}{+45} \color{blue}{-45} \color{blue}{-144x} & = & \color{red}{144x} +14 \color{blue}{-144x} \color{blue}{-45} \\\Leftrightarrow & -270x-144x& = & 14-45 \\\Leftrightarrow & \color{red}{-414} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-414} & & \\\Leftrightarrow & x = \frac{31}{414} & & \\ & V = \left\{ \frac{31}{414} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{9})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{-308} & = & \color{red}{-891x} +18 \\\Leftrightarrow & 2772x \color{red}{-308} \color{blue}{+308} \color{blue}{+891x} & = & \color{red}{-891x} +18 \color{blue}{+891x} \color{blue}{+308} \\\Leftrightarrow & 2772x+891x& = & 18+308 \\\Leftrightarrow & \color{red}{3663} x& = & 326 \\\Leftrightarrow & x = \frac{326}{3663} & & \\ & V = \left\{ \frac{326}{3663} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{105x} +35 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -300x-105x& = & 35-36 \\\Leftrightarrow & \color{red}{-405} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-405} & & \\\Leftrightarrow & x = \frac{1}{405} & & \\ & V = \left\{ \frac{1}{405} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{9})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{10}{9}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x- \frac{100}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{-100} & = & \color{red}{-630x} +81 \\\Leftrightarrow & -1800x \color{red}{-100} \color{blue}{+100} \color{blue}{+630x} & = & \color{red}{-630x} +81 \color{blue}{+630x} \color{blue}{+100} \\\Leftrightarrow & -1800x+630x& = & 81+100 \\\Leftrightarrow & \color{red}{-1170} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1170} & & \\\Leftrightarrow & x = \frac{-181}{1170} & & \\ & V = \left\{ \frac{-181}{1170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{6})& = & 9x+\frac{5}{8} \\\Leftrightarrow & -20x+\frac{25}{6}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{100}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+100} & = & \color{red}{216x} +15 \\\Leftrightarrow & -480x \color{red}{+100} \color{blue}{-100} \color{blue}{-216x} & = & \color{red}{216x} +15 \color{blue}{-216x} \color{blue}{-100} \\\Leftrightarrow & -480x-216x& = & 15-100 \\\Leftrightarrow & \color{red}{-696} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-696} & & \\\Leftrightarrow & x = \frac{85}{696} & & \\ & V = \left\{ \frac{85}{696} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1800}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1800x \color{red}{+144} & = & \color{red}{420x} +25 \\\Leftrightarrow & -1800x \color{red}{+144} \color{blue}{-144} \color{blue}{-420x} & = & \color{red}{420x} +25 \color{blue}{-420x} \color{blue}{-144} \\\Leftrightarrow & -1800x-420x& = & 25-144 \\\Leftrightarrow & \color{red}{-2220} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-2220} & & \\\Leftrightarrow & x = \frac{119}{2220} & & \\ & V = \left\{ \frac{119}{2220} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{100x} +45 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{-96} \\\Leftrightarrow & 480x-100x& = & 45-96 \\\Leftrightarrow & \color{red}{380} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{380} & & \\ & V = \left\{ \frac{-51}{380} \right\} & \\\end{align}\)
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