Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-120} & = & \color{red}{140x} +63 \\\Leftrightarrow & 336x \color{red}{-120} \color{blue}{+120} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+120} \\\Leftrightarrow & 336x-140x& = & 63+120 \\\Leftrightarrow & \color{red}{196} x& = & 183 \\\Leftrightarrow & x = \frac{183}{196} & & \\ & V = \left\{ \frac{183}{196} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-40} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -270x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & -270x+315x& = & 54+40 \\\Leftrightarrow & \color{red}{45} x& = & 94 \\\Leftrightarrow & x = \frac{94}{45} & & \\ & V = \left\{ \frac{94}{45} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-40} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 150x \color{red}{-40} \color{blue}{+40} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{+40} \\\Leftrightarrow & 150x+45x& = & 18+40 \\\Leftrightarrow & \color{red}{195} x& = & 58 \\\Leftrightarrow & x = \frac{58}{195} & & \\ & V = \left\{ \frac{58}{195} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{10})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 9x-\frac{9}{10}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{-27} & = & \color{red}{120x} +100 \\\Leftrightarrow & 270x \color{red}{-27} \color{blue}{+27} \color{blue}{-120x} & = & \color{red}{120x} +100 \color{blue}{-120x} \color{blue}{+27} \\\Leftrightarrow & 270x-120x& = & 100+27 \\\Leftrightarrow & \color{red}{150} x& = & 127 \\\Leftrightarrow & x = \frac{127}{150} & & \\ & V = \left\{ \frac{127}{150} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 4x+\frac{2}{11} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-12} & = & \color{red}{44x} +2 \\\Leftrightarrow & 165x \color{red}{-12} \color{blue}{+12} \color{blue}{-44x} & = & \color{red}{44x} +2 \color{blue}{-44x} \color{blue}{+12} \\\Leftrightarrow & 165x-44x& = & 2+12 \\\Leftrightarrow & \color{red}{121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{121} & & \\ & V = \left\{ \frac{14}{121} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-264} & = & \color{red}{440x} +25 \\\Leftrightarrow & -990x \color{red}{-264} \color{blue}{+264} \color{blue}{-440x} & = & \color{red}{440x} +25 \color{blue}{-440x} \color{blue}{+264} \\\Leftrightarrow & -990x-440x& = & 25+264 \\\Leftrightarrow & \color{red}{-1430} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-1430} & & \\\Leftrightarrow & x = \frac{-289}{1430} & & \\ & V = \left\{ \frac{-289}{1430} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{2})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{35}{2}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x- \frac{175}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{-175} & = & \color{red}{20x} +12 \\\Leftrightarrow & 350x \color{red}{-175} \color{blue}{+175} \color{blue}{-20x} & = & \color{red}{20x} +12 \color{blue}{-20x} \color{blue}{+175} \\\Leftrightarrow & 350x-20x& = & 12+175 \\\Leftrightarrow & \color{red}{330} x& = & 187 \\\Leftrightarrow & x = \frac{187}{330} & & \\\Leftrightarrow & x = \frac{17}{30} & & \\ & V = \left\{ \frac{17}{30} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-180} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 1008x \color{red}{-180} \color{blue}{+180} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+180} \\\Leftrightarrow & 1008x+315x& = & 14+180 \\\Leftrightarrow & \color{red}{1323} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1323} & & \\ & V = \left\{ \frac{194}{1323} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+72} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 180x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & 180x+75x& = & 20-72 \\\Leftrightarrow & \color{red}{255} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{255} & & \\ & V = \left\{ \frac{-52}{255} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{12})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -35x+\frac{35}{12}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-2940}{ \color{blue}{84} }x+ \frac{245}{ \color{blue}{84} })& = & (\frac{252}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -2940x \color{red}{+245} & = & \color{red}{252x} +72 \\\Leftrightarrow & -2940x \color{red}{+245} \color{blue}{-245} \color{blue}{-252x} & = & \color{red}{252x} +72 \color{blue}{-252x} \color{blue}{-245} \\\Leftrightarrow & -2940x-252x& = & 72-245 \\\Leftrightarrow & \color{red}{-3192} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-3192} & & \\\Leftrightarrow & x = \frac{173}{3192} & & \\ & V = \left\{ \frac{173}{3192} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-56} & = & \color{red}{-441x} +18 \\\Leftrightarrow & -630x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +18 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & -630x+441x& = & 18+56 \\\Leftrightarrow & \color{red}{-189} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-189} & & \\\Leftrightarrow & x = \frac{-74}{189} & & \\ & V = \left\{ \frac{-74}{189} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+100} & = & \color{red}{-105x} +27 \\\Leftrightarrow & -150x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +27 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -150x+105x& = & 27-100 \\\Leftrightarrow & \color{red}{-45} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-45} & & \\\Leftrightarrow & x = \frac{73}{45} & & \\ & V = \left\{ \frac{73}{45} \right\} & \\\end{align}\)
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