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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{7})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -15x+\frac{9}{7}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+18} & = & \color{red}{-112x} +35 \\\Leftrightarrow & -210x \color{red}{+18} \color{blue}{-18} \color{blue}{+112x} & = & \color{red}{-112x} +35 \color{blue}{+112x} \color{blue}{-18} \\\Leftrightarrow & -210x+112x& = & 35-18 \\\Leftrightarrow & \color{red}{-98} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-98} & & \\\Leftrightarrow & x = \frac{-17}{98} & & \\ & V = \left\{ \frac{-17}{98} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 8x+\frac{8}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+16} & = & \color{red}{50x} +9 \\\Leftrightarrow & 80x \color{red}{+16} \color{blue}{-16} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{-16} \\\Leftrightarrow & 80x-50x& = & 9-16 \\\Leftrightarrow & \color{red}{30} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{30} & & \\ & V = \left\{ \frac{-7}{30} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-88} & = & \color{red}{-693x} +72 \\\Leftrightarrow & -990x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +72 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -990x+693x& = & 72+88 \\\Leftrightarrow & \color{red}{-297} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-297} & & \\\Leftrightarrow & x = \frac{-160}{297} & & \\ & V = \left\{ \frac{-160}{297} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{-24} & = & \color{red}{-50x} +9 \\\Leftrightarrow & 180x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 180x+50x& = & 9+24 \\\Leftrightarrow & \color{red}{230} x& = & 33 \\\Leftrightarrow & x = \frac{33}{230} & & \\ & V = \left\{ \frac{33}{230} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-168} & = & \color{red}{315x} +45 \\\Leftrightarrow & -630x \color{red}{-168} \color{blue}{+168} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{+168} \\\Leftrightarrow & -630x-315x& = & 45+168 \\\Leftrightarrow & \color{red}{-945} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-945} & & \\\Leftrightarrow & x = \frac{-71}{315} & & \\ & V = \left\{ \frac{-71}{315} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{11})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 21x+\frac{14}{11}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1617}{ \color{blue}{77} }x+ \frac{98}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1617x \color{red}{+98} & = & \color{red}{308x} +22 \\\Leftrightarrow & 1617x \color{red}{+98} \color{blue}{-98} \color{blue}{-308x} & = & \color{red}{308x} +22 \color{blue}{-308x} \color{blue}{-98} \\\Leftrightarrow & 1617x-308x& = & 22-98 \\\Leftrightarrow & \color{red}{1309} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{1309} & & \\ & V = \left\{ \frac{-76}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{20}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-20} & = & \color{red}{15x} +10 \\\Leftrightarrow & 36x \color{red}{-20} \color{blue}{+20} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{+20} \\\Leftrightarrow & 36x-15x& = & 10+20 \\\Leftrightarrow & \color{red}{21} x& = & 30 \\\Leftrightarrow & x = \frac{30}{21} & & \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{9})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 14x+\frac{14}{9}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x+ \frac{98}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{+98} & = & \color{red}{-315x} +81 \\\Leftrightarrow & 882x \color{red}{+98} \color{blue}{-98} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{-98} \\\Leftrightarrow & 882x+315x& = & 81-98 \\\Leftrightarrow & \color{red}{1197} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{1197} & & \\ & V = \left\{ \frac{-17}{1197} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{30}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+210} & = & \color{red}{-385x} +110 \\\Leftrightarrow & -1848x \color{red}{+210} \color{blue}{-210} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-210} \\\Leftrightarrow & -1848x+385x& = & 110-210 \\\Leftrightarrow & \color{red}{-1463} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-1463} & & \\\Leftrightarrow & x = \frac{100}{1463} & & \\ & V = \left\{ \frac{100}{1463} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{+231} & = & \color{red}{-704x} +48 \\\Leftrightarrow & -1848x \color{red}{+231} \color{blue}{-231} \color{blue}{+704x} & = & \color{red}{-704x} +48 \color{blue}{+704x} \color{blue}{-231} \\\Leftrightarrow & -1848x+704x& = & 48-231 \\\Leftrightarrow & \color{red}{-1144} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{-1144} & & \\\Leftrightarrow & x = \frac{183}{1144} & & \\ & V = \left\{ \frac{183}{1144} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{140x} +21 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & 168x-140x& = & 21-24 \\\Leftrightarrow & \color{red}{28} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -60x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & -60x+70x& = & 45+24 \\\Leftrightarrow & \color{red}{10} x& = & 69 \\\Leftrightarrow & x = \frac{69}{10} & & \\ & V = \left\{ \frac{69}{10} \right\} & \\\end{align}\)
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