Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{20}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-20} & = & \color{red}{81x} +6 \\\Leftrightarrow & 90x \color{red}{-20} \color{blue}{+20} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{+20} \\\Leftrightarrow & 90x-81x& = & 6+20 \\\Leftrightarrow & \color{red}{9} x& = & 26 \\\Leftrightarrow & x = \frac{26}{9} & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{12})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 28x-\frac{35}{12}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2352}{ \color{blue}{84} }x- \frac{245}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{96}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2352x \color{red}{-245} & = & \color{red}{-252x} +96 \\\Leftrightarrow & 2352x \color{red}{-245} \color{blue}{+245} \color{blue}{+252x} & = & \color{red}{-252x} +96 \color{blue}{+252x} \color{blue}{+245} \\\Leftrightarrow & 2352x+252x& = & 96+245 \\\Leftrightarrow & \color{red}{2604} x& = & 341 \\\Leftrightarrow & x = \frac{341}{2604} & & \\\Leftrightarrow & x = \frac{11}{84} & & \\ & V = \left\{ \frac{11}{84} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{4})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -9x+\frac{9}{4}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{+27} & = & \color{red}{60x} +40 \\\Leftrightarrow & -108x \color{red}{+27} \color{blue}{-27} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{-27} \\\Leftrightarrow & -108x-60x& = & 40-27 \\\Leftrightarrow & \color{red}{-168} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-168} & & \\\Leftrightarrow & x = \frac{-13}{168} & & \\ & V = \left\{ \frac{-13}{168} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{2})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x+\frac{35}{2}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{+175} & = & \color{red}{-30x} +16 \\\Leftrightarrow & -140x \color{red}{+175} \color{blue}{-175} \color{blue}{+30x} & = & \color{red}{-30x} +16 \color{blue}{+30x} \color{blue}{-175} \\\Leftrightarrow & -140x+30x& = & 16-175 \\\Leftrightarrow & \color{red}{-110} x& = & -159 \\\Leftrightarrow & x = \frac{-159}{-110} & & \\\Leftrightarrow & x = \frac{159}{110} & & \\ & V = \left\{ \frac{159}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-10} & = & \color{red}{63x} +2 \\\Leftrightarrow & -56x \color{red}{-10} \color{blue}{+10} \color{blue}{-63x} & = & \color{red}{63x} +2 \color{blue}{-63x} \color{blue}{+10} \\\Leftrightarrow & -56x-63x& = & 2+10 \\\Leftrightarrow & \color{red}{-119} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-119} & & \\\Leftrightarrow & x = \frac{-12}{119} & & \\ & V = \left\{ \frac{-12}{119} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{15}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+15} & = & \color{red}{55x} +5 \\\Leftrightarrow & 66x \color{red}{+15} \color{blue}{-15} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-15} \\\Leftrightarrow & 66x-55x& = & 5-15 \\\Leftrightarrow & \color{red}{11} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{-175x} +28 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & -420x+175x& = & 28-150 \\\Leftrightarrow & \color{red}{-245} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-245} & & \\\Leftrightarrow & x = \frac{122}{245} & & \\ & V = \left\{ \frac{122}{245} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{50x} +7 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +7 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -90x-50x& = & 7+24 \\\Leftrightarrow & \color{red}{-140} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-140} & & \\\Leftrightarrow & x = \frac{-31}{140} & & \\ & V = \left\{ \frac{-31}{140} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{6})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-25} & = & \color{red}{42x} +5 \\\Leftrightarrow & 90x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & 90x-42x& = & 5+25 \\\Leftrightarrow & \color{red}{48} x& = & 30 \\\Leftrightarrow & x = \frac{30}{48} & & \\\Leftrightarrow & x = \frac{5}{8} & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-126} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & -924x-385x& = & 110+126 \\\Leftrightarrow & \color{red}{-1309} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1309} & & \\\Leftrightarrow & x = \frac{-236}{1309} & & \\ & V = \left\{ \frac{-236}{1309} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{5})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 28x-\frac{14}{5}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{980}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 980x \color{red}{-98} & = & \color{red}{-315x} +45 \\\Leftrightarrow & 980x \color{red}{-98} \color{blue}{+98} \color{blue}{+315x} & = & \color{red}{-315x} +45 \color{blue}{+315x} \color{blue}{+98} \\\Leftrightarrow & 980x+315x& = & 45+98 \\\Leftrightarrow & \color{red}{1295} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1295} & & \\ & V = \left\{ \frac{143}{1295} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{7}{5} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+12} & = & \color{red}{15x} +7 \\\Leftrightarrow & 40x \color{red}{+12} \color{blue}{-12} \color{blue}{-15x} & = & \color{red}{15x} +7 \color{blue}{-15x} \color{blue}{-12} \\\Leftrightarrow & 40x-15x& = & 7-12 \\\Leftrightarrow & \color{red}{25} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{25} & & \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
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