Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{165x} +30 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{-132} \\\Leftrightarrow & 880x-165x& = & 30-132 \\\Leftrightarrow & \color{red}{715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{715} & & \\ & V = \left\{ \frac{-102}{715} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{9}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-27} & = & \color{red}{75x} +20 \\\Leftrightarrow & -180x \color{red}{-27} \color{blue}{+27} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+27} \\\Leftrightarrow & -180x-75x& = & 20+27 \\\Leftrightarrow & \color{red}{-255} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-255} & & \\\Leftrightarrow & x = \frac{-47}{255} & & \\ & V = \left\{ \frac{-47}{255} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-108} & = & \color{red}{315x} +35 \\\Leftrightarrow & 1350x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & 1350x-315x& = & 35+108 \\\Leftrightarrow & \color{red}{1035} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1035} & & \\ & V = \left\{ \frac{143}{1035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{6}{5}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{160x} +15 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{-160x} & = & \color{red}{160x} +15 \color{blue}{-160x} \color{blue}{-24} \\\Leftrightarrow & -300x-160x& = & 15-24 \\\Leftrightarrow & \color{red}{-460} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-460} & & \\\Leftrightarrow & x = \frac{9}{460} & & \\ & V = \left\{ \frac{9}{460} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{245x} +42 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+100} \\\Leftrightarrow & 560x-245x& = & 42+100 \\\Leftrightarrow & \color{red}{315} x& = & 142 \\\Leftrightarrow & x = \frac{142}{315} & & \\ & V = \left\{ \frac{142}{315} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+50} & = & \color{red}{245x} +56 \\\Leftrightarrow & 280x \color{red}{+50} \color{blue}{-50} \color{blue}{-245x} & = & \color{red}{245x} +56 \color{blue}{-245x} \color{blue}{-50} \\\Leftrightarrow & 280x-245x& = & 56-50 \\\Leftrightarrow & \color{red}{35} x& = & 6 \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{18}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{50x} +9 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{-36} \\\Leftrightarrow & -120x-50x& = & 9-36 \\\Leftrightarrow & \color{red}{-170} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-170} & & \\\Leftrightarrow & x = \frac{27}{170} & & \\ & V = \left\{ \frac{27}{170} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{9})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -20x-\frac{20}{9}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-80} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -720x \color{red}{-80} \color{blue}{+80} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{+80} \\\Leftrightarrow & -720x+252x& = & 63+80 \\\Leftrightarrow & \color{red}{-468} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-468} & & \\\Leftrightarrow & x = \frac{-11}{36} & & \\ & V = \left\{ \frac{-11}{36} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{8})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 14x+\frac{35}{8}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x+ \frac{175}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{+175} & = & \color{red}{-360x} +48 \\\Leftrightarrow & 560x \color{red}{+175} \color{blue}{-175} \color{blue}{+360x} & = & \color{red}{-360x} +48 \color{blue}{+360x} \color{blue}{-175} \\\Leftrightarrow & 560x+360x& = & 48-175 \\\Leftrightarrow & \color{red}{920} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{920} & & \\ & V = \left\{ \frac{-127}{920} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x-\frac{8}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-8} & = & \color{red}{55x} +7 \\\Leftrightarrow & -132x \color{red}{-8} \color{blue}{+8} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{+8} \\\Leftrightarrow & -132x-55x& = & 7+8 \\\Leftrightarrow & \color{red}{-187} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-187} & & \\\Leftrightarrow & x = \frac{-15}{187} & & \\ & V = \left\{ \frac{-15}{187} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -10x+\frac{25}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+25} & = & \color{red}{77x} +4 \\\Leftrightarrow & -110x \color{red}{+25} \color{blue}{-25} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-25} \\\Leftrightarrow & -110x-77x& = & 4-25 \\\Leftrightarrow & \color{red}{-187} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-187} & & \\\Leftrightarrow & x = \frac{21}{187} & & \\ & V = \left\{ \frac{21}{187} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{12})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{25}{12}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-25} & = & \color{red}{36x} +40 \\\Leftrightarrow & -240x \color{red}{-25} \color{blue}{+25} \color{blue}{-36x} & = & \color{red}{36x} +40 \color{blue}{-36x} \color{blue}{+25} \\\Leftrightarrow & -240x-36x& = & 40+25 \\\Leftrightarrow & \color{red}{-276} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-276} & & \\\Leftrightarrow & x = \frac{-65}{276} & & \\ & V = \left\{ \frac{-65}{276} \right\} & \\\end{align}\)
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