Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 15x+\frac{25}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{125}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+125} & = & \color{red}{-245x} +28 \\\Leftrightarrow & 525x \color{red}{+125} \color{blue}{-125} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-125} \\\Leftrightarrow & 525x+245x& = & 28-125 \\\Leftrightarrow & \color{red}{770} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{770} & & \\ & V = \left\{ \frac{-97}{770} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{7})& = & -9x+\frac{7}{9} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-144} & = & \color{red}{-567x} +49 \\\Leftrightarrow & -504x \color{red}{-144} \color{blue}{+144} \color{blue}{+567x} & = & \color{red}{-567x} +49 \color{blue}{+567x} \color{blue}{+144} \\\Leftrightarrow & -504x+567x& = & 49+144 \\\Leftrightarrow & \color{red}{63} x& = & 193 \\\Leftrightarrow & x = \frac{193}{63} & & \\ & V = \left\{ \frac{193}{63} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{160x} +24 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{-160x} & = & \color{red}{160x} +24 \color{blue}{-160x} \color{blue}{+75} \\\Leftrightarrow & 300x-160x& = & 24+75 \\\Leftrightarrow & \color{red}{140} x& = & 99 \\\Leftrightarrow & x = \frac{99}{140} & & \\ & V = \left\{ \frac{99}{140} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -5x+\frac{5}{8} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-504}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -504x \color{red}{-48} & = & \color{red}{-280x} +35 \\\Leftrightarrow & -504x \color{red}{-48} \color{blue}{+48} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+48} \\\Leftrightarrow & -504x+280x& = & 35+48 \\\Leftrightarrow & \color{red}{-224} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-224} & & \\\Leftrightarrow & x = \frac{-83}{224} & & \\ & V = \left\{ \frac{-83}{224} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-196x} +35 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{+40} \\\Leftrightarrow & -280x+196x& = & 35+40 \\\Leftrightarrow & \color{red}{-84} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-84} & & \\\Leftrightarrow & x = \frac{-25}{28} & & \\ & V = \left\{ \frac{-25}{28} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{8}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+8} & = & \color{red}{33x} +4 \\\Leftrightarrow & 176x \color{red}{+8} \color{blue}{-8} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{-8} \\\Leftrightarrow & 176x-33x& = & 4-8 \\\Leftrightarrow & \color{red}{143} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{143} & & \\ & V = \left\{ \frac{-4}{143} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{5})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 28x+\frac{28}{5}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1120}{ \color{blue}{40} }x+ \frac{224}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1120x \color{red}{+224} & = & \color{red}{-360x} +35 \\\Leftrightarrow & 1120x \color{red}{+224} \color{blue}{-224} \color{blue}{+360x} & = & \color{red}{-360x} +35 \color{blue}{+360x} \color{blue}{-224} \\\Leftrightarrow & 1120x+360x& = & 35-224 \\\Leftrightarrow & \color{red}{1480} x& = & -189 \\\Leftrightarrow & x = \frac{-189}{1480} & & \\ & V = \left\{ \frac{-189}{1480} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{9})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 10x+\frac{20}{9}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+140} & = & \color{red}{-441x} +81 \\\Leftrightarrow & 630x \color{red}{+140} \color{blue}{-140} \color{blue}{+441x} & = & \color{red}{-441x} +81 \color{blue}{+441x} \color{blue}{-140} \\\Leftrightarrow & 630x+441x& = & 81-140 \\\Leftrightarrow & \color{red}{1071} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{1071} & & \\ & V = \left\{ \frac{-59}{1071} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{3})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{20}{3}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-140} & = & \color{red}{-147x} +6 \\\Leftrightarrow & -210x \color{red}{-140} \color{blue}{+140} \color{blue}{+147x} & = & \color{red}{-147x} +6 \color{blue}{+147x} \color{blue}{+140} \\\Leftrightarrow & -210x+147x& = & 6+140 \\\Leftrightarrow & \color{red}{-63} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-63} & & \\\Leftrightarrow & x = \frac{-146}{63} & & \\ & V = \left\{ \frac{-146}{63} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{6}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+12} \\\Leftrightarrow & -90x+50x& = & 15+12 \\\Leftrightarrow & \color{red}{-40} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-40} & & \\\Leftrightarrow & x = \frac{-27}{40} & & \\ & V = \left\{ \frac{-27}{40} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{24}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{240}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-240} & = & \color{red}{-550x} +99 \\\Leftrightarrow & -1320x \color{red}{-240} \color{blue}{+240} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{+240} \\\Leftrightarrow & -1320x+550x& = & 99+240 \\\Leftrightarrow & \color{red}{-770} x& = & 339 \\\Leftrightarrow & x = \frac{339}{-770} & & \\\Leftrightarrow & x = \frac{-339}{770} & & \\ & V = \left\{ \frac{-339}{770} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+88} & = & \color{red}{297x} +36 \\\Leftrightarrow & 792x \color{red}{+88} \color{blue}{-88} \color{blue}{-297x} & = & \color{red}{297x} +36 \color{blue}{-297x} \color{blue}{-88} \\\Leftrightarrow & 792x-297x& = & 36-88 \\\Leftrightarrow & \color{red}{495} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{495} & & \\ & V = \left\{ \frac{-52}{495} \right\} & \\\end{align}\)
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