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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-20} & = & \color{red}{154x} +33 \\\Leftrightarrow & -220x \color{red}{-20} \color{blue}{+20} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+20} \\\Leftrightarrow & -220x-154x& = & 33+20 \\\Leftrightarrow & \color{red}{-374} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-374} & & \\\Leftrightarrow & x = \frac{-53}{374} & & \\ & V = \left\{ \frac{-53}{374} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 210x+175x& = & 15-84 \\\Leftrightarrow & \color{red}{385} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{385} & & \\ & V = \left\{ \frac{-69}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+60} \\\Leftrightarrow & 420x-175x& = & 42+60 \\\Leftrightarrow & \color{red}{245} x& = & 102 \\\Leftrightarrow & x = \frac{102}{245} & & \\ & V = \left\{ \frac{102}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{7})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{12}{7}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+48} & = & \color{red}{84x} +63 \\\Leftrightarrow & -560x \color{red}{+48} \color{blue}{-48} \color{blue}{-84x} & = & \color{red}{84x} +63 \color{blue}{-84x} \color{blue}{-48} \\\Leftrightarrow & -560x-84x& = & 63-48 \\\Leftrightarrow & \color{red}{-644} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-644} & & \\\Leftrightarrow & x = \frac{-15}{644} & & \\ & V = \left\{ \frac{-15}{644} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{2})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{9}{2}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-63} & = & \color{red}{-70x} +16 \\\Leftrightarrow & 168x \color{red}{-63} \color{blue}{+63} \color{blue}{+70x} & = & \color{red}{-70x} +16 \color{blue}{+70x} \color{blue}{+63} \\\Leftrightarrow & 168x+70x& = & 16+63 \\\Leftrightarrow & \color{red}{238} x& = & 79 \\\Leftrightarrow & x = \frac{79}{238} & & \\ & V = \left\{ \frac{79}{238} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{7})& = & 2x+\frac{4}{11} \\\Leftrightarrow & 25x+\frac{20}{7}& = & 2x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+220} & = & \color{red}{154x} +28 \\\Leftrightarrow & 1925x \color{red}{+220} \color{blue}{-220} \color{blue}{-154x} & = & \color{red}{154x} +28 \color{blue}{-154x} \color{blue}{-220} \\\Leftrightarrow & 1925x-154x& = & 28-220 \\\Leftrightarrow & \color{red}{1771} x& = & -192 \\\Leftrightarrow & x = \frac{-192}{1771} & & \\ & V = \left\{ \frac{-192}{1771} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 20x+\frac{10}{11}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{+80} & = & \color{red}{792x} +55 \\\Leftrightarrow & 1760x \color{red}{+80} \color{blue}{-80} \color{blue}{-792x} & = & \color{red}{792x} +55 \color{blue}{-792x} \color{blue}{-80} \\\Leftrightarrow & 1760x-792x& = & 55-80 \\\Leftrightarrow & \color{red}{968} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{968} & & \\ & V = \left\{ \frac{-25}{968} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+49} & = & \color{red}{-189x} +30 \\\Leftrightarrow & 735x \color{red}{+49} \color{blue}{-49} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{-49} \\\Leftrightarrow & 735x+189x& = & 30-49 \\\Leftrightarrow & \color{red}{924} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{924} & & \\ & V = \left\{ \frac{-19}{924} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-60} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & -168x+70x& = & 63+60 \\\Leftrightarrow & \color{red}{-98} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-98} & & \\\Leftrightarrow & x = \frac{-123}{98} & & \\ & V = \left\{ \frac{-123}{98} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+264} & = & \color{red}{275x} +20 \\\Leftrightarrow & -1320x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & -1320x-275x& = & 20-264 \\\Leftrightarrow & \color{red}{-1595} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{-1595} & & \\\Leftrightarrow & x = \frac{244}{1595} & & \\ & V = \left\{ \frac{244}{1595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 14+110 \\\Leftrightarrow & \color{red}{-231} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-231} & & \\\Leftrightarrow & x = \frac{-124}{231} & & \\ & V = \left\{ \frac{-124}{231} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{9})& = & 3x+\frac{9}{5} \\\Leftrightarrow & 14x+\frac{35}{9}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x+ \frac{175}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{+175} & = & \color{red}{135x} +81 \\\Leftrightarrow & 630x \color{red}{+175} \color{blue}{-175} \color{blue}{-135x} & = & \color{red}{135x} +81 \color{blue}{-135x} \color{blue}{-175} \\\Leftrightarrow & 630x-135x& = & 81-175 \\\Leftrightarrow & \color{red}{495} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{495} & & \\ & V = \left\{ \frac{-94}{495} \right\} & \\\end{align}\)
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