Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -8x+\frac{7}{10} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{-28} & = & \color{red}{-80x} +7 \\\Leftrightarrow & -280x \color{red}{-28} \color{blue}{+28} \color{blue}{+80x} & = & \color{red}{-80x} +7 \color{blue}{+80x} \color{blue}{+28} \\\Leftrightarrow & -280x+80x& = & 7+28 \\\Leftrightarrow & \color{red}{-200} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-200} & & \\\Leftrightarrow & x = \frac{-7}{40} & & \\ & V = \left\{ \frac{-7}{40} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-20} \\\Leftrightarrow & -180x+63x& = & 4-20 \\\Leftrightarrow & \color{red}{-117} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-117} & & \\\Leftrightarrow & x = \frac{16}{117} & & \\ & V = \left\{ \frac{16}{117} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{567x} +14 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{-567x} & = & \color{red}{567x} +14 \color{blue}{-567x} \color{blue}{-180} \\\Leftrightarrow & 1260x-567x& = & 14-180 \\\Leftrightarrow & \color{red}{693} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{693} & & \\ & V = \left\{ \frac{-166}{693} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{25}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{175}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-175} & = & \color{red}{147x} +30 \\\Leftrightarrow & 210x \color{red}{-175} \color{blue}{+175} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{+175} \\\Leftrightarrow & 210x-147x& = & 30+175 \\\Leftrightarrow & \color{red}{63} x& = & 205 \\\Leftrightarrow & x = \frac{205}{63} & & \\ & V = \left\{ \frac{205}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+20} & = & \color{red}{-42x} +49 \\\Leftrightarrow & -112x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +49 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & -112x+42x& = & 49-20 \\\Leftrightarrow & \color{red}{-70} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-70} & & \\\Leftrightarrow & x = \frac{-29}{70} & & \\ & V = \left\{ \frac{-29}{70} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -8x+\frac{9}{10} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{-105} & = & \color{red}{-320x} +36 \\\Leftrightarrow & 1400x \color{red}{-105} \color{blue}{+105} \color{blue}{+320x} & = & \color{red}{-320x} +36 \color{blue}{+320x} \color{blue}{+105} \\\Leftrightarrow & 1400x+320x& = & 36+105 \\\Leftrightarrow & \color{red}{1720} x& = & 141 \\\Leftrightarrow & x = \frac{141}{1720} & & \\ & V = \left\{ \frac{141}{1720} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{+24} & = & \color{red}{84x} +21 \\\Leftrightarrow & 112x \color{red}{+24} \color{blue}{-24} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{-24} \\\Leftrightarrow & 112x-84x& = & 21-24 \\\Leftrightarrow & \color{red}{28} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{175}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{40}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+175} & = & \color{red}{392x} +40 \\\Leftrightarrow & 1120x \color{red}{+175} \color{blue}{-175} \color{blue}{-392x} & = & \color{red}{392x} +40 \color{blue}{-392x} \color{blue}{-175} \\\Leftrightarrow & 1120x-392x& = & 40-175 \\\Leftrightarrow & \color{red}{728} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{728} & & \\ & V = \left\{ \frac{-135}{728} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-30} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -126x \color{red}{-30} \color{blue}{+30} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+30} \\\Leftrightarrow & -126x+147x& = & 56+30 \\\Leftrightarrow & \color{red}{21} x& = & 86 \\\Leftrightarrow & x = \frac{86}{21} & & \\ & V = \left\{ \frac{86}{21} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-8} & = & \color{red}{-45x} +12 \\\Leftrightarrow & 108x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +12 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & 108x+45x& = & 12+8 \\\Leftrightarrow & \color{red}{153} x& = & 20 \\\Leftrightarrow & x = \frac{20}{153} & & \\ & V = \left\{ \frac{20}{153} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-63} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -315x \color{red}{-63} \color{blue}{+63} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+63} \\\Leftrightarrow & -315x+175x& = & 20+63 \\\Leftrightarrow & \color{red}{-140} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-140} & & \\\Leftrightarrow & x = \frac{-83}{140} & & \\ & V = \left\{ \frac{-83}{140} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+70} & = & \color{red}{-189x} +27 \\\Leftrightarrow & 210x \color{red}{+70} \color{blue}{-70} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{-70} \\\Leftrightarrow & 210x+189x& = & 27-70 \\\Leftrightarrow & \color{red}{399} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{399} & & \\ & V = \left\{ \frac{-43}{399} \right\} & \\\end{align}\)
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