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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{10})& = & -8x+\frac{6}{7} \\\Leftrightarrow & -28x+\frac{21}{10}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1960}{ \color{blue}{70} }x+ \frac{147}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1960x \color{red}{+147} & = & \color{red}{-560x} +60 \\\Leftrightarrow & -1960x \color{red}{+147} \color{blue}{-147} \color{blue}{+560x} & = & \color{red}{-560x} +60 \color{blue}{+560x} \color{blue}{-147} \\\Leftrightarrow & -1960x+560x& = & 60-147 \\\Leftrightarrow & \color{red}{-1400} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-1400} & & \\\Leftrightarrow & x = \frac{87}{1400} & & \\ & V = \left\{ \frac{87}{1400} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{3})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -20x+\frac{16}{3}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+80} & = & \color{red}{-105x} +9 \\\Leftrightarrow & -300x \color{red}{+80} \color{blue}{-80} \color{blue}{+105x} & = & \color{red}{-105x} +9 \color{blue}{+105x} \color{blue}{-80} \\\Leftrightarrow & -300x+105x& = & 9-80 \\\Leftrightarrow & \color{red}{-195} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-195} & & \\\Leftrightarrow & x = \frac{71}{195} & & \\ & V = \left\{ \frac{71}{195} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-75} & = & \color{red}{160x} +12 \\\Leftrightarrow & -500x \color{red}{-75} \color{blue}{+75} \color{blue}{-160x} & = & \color{red}{160x} +12 \color{blue}{-160x} \color{blue}{+75} \\\Leftrightarrow & -500x-160x& = & 12+75 \\\Leftrightarrow & \color{red}{-660} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-660} & & \\\Leftrightarrow & x = \frac{-29}{220} & & \\ & V = \left\{ \frac{-29}{220} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -16x-\frac{20}{7}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-896}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -896x \color{red}{-160} & = & \color{red}{392x} +35 \\\Leftrightarrow & -896x \color{red}{-160} \color{blue}{+160} \color{blue}{-392x} & = & \color{red}{392x} +35 \color{blue}{-392x} \color{blue}{+160} \\\Leftrightarrow & -896x-392x& = & 35+160 \\\Leftrightarrow & \color{red}{-1288} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-1288} & & \\\Leftrightarrow & x = \frac{-195}{1288} & & \\ & V = \left\{ \frac{-195}{1288} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -24x-\frac{30}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-210} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -1848x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & -1848x+385x& = & 44+210 \\\Leftrightarrow & \color{red}{-1463} x& = & 254 \\\Leftrightarrow & x = \frac{254}{-1463} & & \\\Leftrightarrow & x = \frac{-254}{1463} & & \\ & V = \left\{ \frac{-254}{1463} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{11})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{12}{11}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+84} & = & \color{red}{616x} +110 \\\Leftrightarrow & -1155x \color{red}{+84} \color{blue}{-84} \color{blue}{-616x} & = & \color{red}{616x} +110 \color{blue}{-616x} \color{blue}{-84} \\\Leftrightarrow & -1155x-616x& = & 110-84 \\\Leftrightarrow & \color{red}{-1771} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-1771} & & \\\Leftrightarrow & x = \frac{-26}{1771} & & \\ & V = \left\{ \frac{-26}{1771} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{8})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{15}{8}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+15} & = & \color{red}{40x} +18 \\\Leftrightarrow & -96x \color{red}{+15} \color{blue}{-15} \color{blue}{-40x} & = & \color{red}{40x} +18 \color{blue}{-40x} \color{blue}{-15} \\\Leftrightarrow & -96x-40x& = & 18-15 \\\Leftrightarrow & \color{red}{-136} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-136} & & \\\Leftrightarrow & x = \frac{-3}{136} & & \\ & V = \left\{ \frac{-3}{136} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+168} & = & \color{red}{539x} +22 \\\Leftrightarrow & 1386x \color{red}{+168} \color{blue}{-168} \color{blue}{-539x} & = & \color{red}{539x} +22 \color{blue}{-539x} \color{blue}{-168} \\\Leftrightarrow & 1386x-539x& = & 22-168 \\\Leftrightarrow & \color{red}{847} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{847} & & \\ & V = \left\{ \frac{-146}{847} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{8}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{+80} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -1100x \color{red}{+80} \color{blue}{-80} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{-80} \\\Leftrightarrow & -1100x+770x& = & 33-80 \\\Leftrightarrow & \color{red}{-330} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-330} & & \\\Leftrightarrow & x = \frac{47}{330} & & \\ & V = \left\{ \frac{47}{330} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{405x} +54 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{-405x} & = & \color{red}{405x} +54 \color{blue}{-405x} \color{blue}{+40} \\\Leftrightarrow & 360x-405x& = & 54+40 \\\Leftrightarrow & \color{red}{-45} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-45} & & \\\Leftrightarrow & x = \frac{-94}{45} & & \\ & V = \left\{ \frac{-94}{45} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{10})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{9}{10}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-99} & = & \color{red}{-880x} +60 \\\Leftrightarrow & -1650x \color{red}{-99} \color{blue}{+99} \color{blue}{+880x} & = & \color{red}{-880x} +60 \color{blue}{+880x} \color{blue}{+99} \\\Leftrightarrow & -1650x+880x& = & 60+99 \\\Leftrightarrow & \color{red}{-770} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-770} & & \\\Leftrightarrow & x = \frac{-159}{770} & & \\ & V = \left\{ \frac{-159}{770} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{-693x} +35 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +35 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -308x+693x& = & 35+110 \\\Leftrightarrow & \color{red}{385} x& = & 145 \\\Leftrightarrow & x = \frac{145}{385} & & \\\Leftrightarrow & x = \frac{29}{77} & & \\ & V = \left\{ \frac{29}{77} \right\} & \\\end{align}\)
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