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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{8}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-88} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 220x \color{red}{-88} \color{blue}{+88} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+88} \\\Leftrightarrow & 220x+385x& = & 30+88 \\\Leftrightarrow & \color{red}{605} x& = & 118 \\\Leftrightarrow & x = \frac{118}{605} & & \\ & V = \left\{ \frac{118}{605} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+88} & = & \color{red}{-231x} +30 \\\Leftrightarrow & 330x \color{red}{+88} \color{blue}{-88} \color{blue}{+231x} & = & \color{red}{-231x} +30 \color{blue}{+231x} \color{blue}{-88} \\\Leftrightarrow & 330x+231x& = & 30-88 \\\Leftrightarrow & \color{red}{561} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{561} & & \\ & V = \left\{ \frac{-58}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{8}{9}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{-40} & = & \color{red}{-315x} +36 \\\Leftrightarrow & -900x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +36 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & -900x+315x& = & 36+40 \\\Leftrightarrow & \color{red}{-585} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-585} & & \\\Leftrightarrow & x = \frac{-76}{585} & & \\ & V = \left\{ \frac{-76}{585} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{3})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 14x+\frac{7}{3}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{+70} & = & \color{red}{-270x} +21 \\\Leftrightarrow & 420x \color{red}{+70} \color{blue}{-70} \color{blue}{+270x} & = & \color{red}{-270x} +21 \color{blue}{+270x} \color{blue}{-70} \\\Leftrightarrow & 420x+270x& = & 21-70 \\\Leftrightarrow & \color{red}{690} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{690} & & \\ & V = \left\{ \frac{-49}{690} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{147x} +35 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & 336x-147x& = & 35+48 \\\Leftrightarrow & \color{red}{189} x& = & 83 \\\Leftrightarrow & x = \frac{83}{189} & & \\ & V = \left\{ \frac{83}{189} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+48} & = & \color{red}{-100x} +15 \\\Leftrightarrow & 240x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & 240x+100x& = & 15-48 \\\Leftrightarrow & \color{red}{340} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{340} & & \\ & V = \left\{ \frac{-33}{340} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -10x-\frac{15}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-75} & = & \color{red}{245x} +49 \\\Leftrightarrow & -350x \color{red}{-75} \color{blue}{+75} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+75} \\\Leftrightarrow & -350x-245x& = & 49+75 \\\Leftrightarrow & \color{red}{-595} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-595} & & \\\Leftrightarrow & x = \frac{-124}{595} & & \\ & V = \left\{ \frac{-124}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 14x-\frac{21}{2}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{56}{ \color{blue}{4} }x- \frac{42}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 56x \color{red}{-42} & = & \color{red}{12x} +9 \\\Leftrightarrow & 56x \color{red}{-42} \color{blue}{+42} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{+42} \\\Leftrightarrow & 56x-12x& = & 9+42 \\\Leftrightarrow & \color{red}{44} x& = & 51 \\\Leftrightarrow & x = \frac{51}{44} & & \\ & V = \left\{ \frac{51}{44} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{-48} & = & \color{red}{70x} +25 \\\Leftrightarrow & -300x \color{red}{-48} \color{blue}{+48} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+48} \\\Leftrightarrow & -300x-70x& = & 25+48 \\\Leftrightarrow & \color{red}{-370} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-370} & & \\\Leftrightarrow & x = \frac{-73}{370} & & \\ & V = \left\{ \frac{-73}{370} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{11})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 20x-\frac{20}{11}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-140} & = & \color{red}{231x} +99 \\\Leftrightarrow & 1540x \color{red}{-140} \color{blue}{+140} \color{blue}{-231x} & = & \color{red}{231x} +99 \color{blue}{-231x} \color{blue}{+140} \\\Leftrightarrow & 1540x-231x& = & 99+140 \\\Leftrightarrow & \color{red}{1309} x& = & 239 \\\Leftrightarrow & x = \frac{239}{1309} & & \\ & V = \left\{ \frac{239}{1309} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{7}{6} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-120}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{-120x} +35 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{-72} \\\Leftrightarrow & -450x+120x& = & 35-72 \\\Leftrightarrow & \color{red}{-330} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-330} & & \\\Leftrightarrow & x = \frac{37}{330} & & \\ & V = \left\{ \frac{37}{330} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{11})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -10x-\frac{4}{11}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{12}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-12} & = & \color{red}{-231x} +55 \\\Leftrightarrow & -330x \color{red}{-12} \color{blue}{+12} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{+12} \\\Leftrightarrow & -330x+231x& = & 55+12 \\\Leftrightarrow & \color{red}{-99} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-99} & & \\\Leftrightarrow & x = \frac{-67}{99} & & \\ & V = \left\{ \frac{-67}{99} \right\} & \\\end{align}\)
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