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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{9})& = & 6x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{14}{9}& = & 6x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+14} & = & \color{red}{54x} +30 \\\Leftrightarrow & -252x \color{red}{+14} \color{blue}{-14} \color{blue}{-54x} & = & \color{red}{54x} +30 \color{blue}{-54x} \color{blue}{-14} \\\Leftrightarrow & -252x-54x& = & 30-14 \\\Leftrightarrow & \color{red}{-306} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-306} & & \\\Leftrightarrow & x = \frac{-8}{153} & & \\ & V = \left\{ \frac{-8}{153} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 15x+\frac{10}{11}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{+90} & = & \color{red}{-693x} +77 \\\Leftrightarrow & 1485x \color{red}{+90} \color{blue}{-90} \color{blue}{+693x} & = & \color{red}{-693x} +77 \color{blue}{+693x} \color{blue}{-90} \\\Leftrightarrow & 1485x+693x& = & 77-90 \\\Leftrightarrow & \color{red}{2178} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{2178} & & \\ & V = \left\{ \frac{-13}{2178} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+132} & = & \color{red}{-385x} +15 \\\Leftrightarrow & -330x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +15 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -330x+385x& = & 15-132 \\\Leftrightarrow & \color{red}{55} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{55} & & \\ & V = \left\{ \frac{-117}{55} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{45x} +10 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +10 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & 120x-45x& = & 10-36 \\\Leftrightarrow & \color{red}{75} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{75} & & \\ & V = \left\{ \frac{-26}{75} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+126} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 1386x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & 1386x+385x& = & 33-126 \\\Leftrightarrow & \color{red}{1771} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1771} & & \\ & V = \left\{ \frac{-93}{1771} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+50} & = & \color{red}{495x} +77 \\\Leftrightarrow & -220x \color{red}{+50} \color{blue}{-50} \color{blue}{-495x} & = & \color{red}{495x} +77 \color{blue}{-495x} \color{blue}{-50} \\\Leftrightarrow & -220x-495x& = & 77-50 \\\Leftrightarrow & \color{red}{-715} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-715} & & \\\Leftrightarrow & x = \frac{-27}{715} & & \\ & V = \left\{ \frac{-27}{715} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{11})& = & 3x+\frac{5}{8} \\\Leftrightarrow & -14x+\frac{28}{11}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x+ \frac{224}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{+224} & = & \color{red}{264x} +55 \\\Leftrightarrow & -1232x \color{red}{+224} \color{blue}{-224} \color{blue}{-264x} & = & \color{red}{264x} +55 \color{blue}{-264x} \color{blue}{-224} \\\Leftrightarrow & -1232x-264x& = & 55-224 \\\Leftrightarrow & \color{red}{-1496} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-1496} & & \\\Leftrightarrow & x = \frac{169}{1496} & & \\ & V = \left\{ \frac{169}{1496} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{10}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{-42x} +27 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & -36x+42x& = & 27-20 \\\Leftrightarrow & \color{red}{6} x& = & 7 \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-14} & = & \color{red}{72x} +24 \\\Leftrightarrow & -189x \color{red}{-14} \color{blue}{+14} \color{blue}{-72x} & = & \color{red}{72x} +24 \color{blue}{-72x} \color{blue}{+14} \\\Leftrightarrow & -189x-72x& = & 24+14 \\\Leftrightarrow & \color{red}{-261} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-261} & & \\\Leftrightarrow & x = \frac{-38}{261} & & \\ & V = \left\{ \frac{-38}{261} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{5})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 28x-\frac{21}{5}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x- \frac{189}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{-189} & = & \color{red}{-225x} +20 \\\Leftrightarrow & 1260x \color{red}{-189} \color{blue}{+189} \color{blue}{+225x} & = & \color{red}{-225x} +20 \color{blue}{+225x} \color{blue}{+189} \\\Leftrightarrow & 1260x+225x& = & 20+189 \\\Leftrightarrow & \color{red}{1485} x& = & 209 \\\Leftrightarrow & x = \frac{209}{1485} & & \\\Leftrightarrow & x = \frac{19}{135} & & \\ & V = \left\{ \frac{19}{135} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 990x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 990x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{1375} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1375} & & \\ & V = \left\{ \frac{162}{1375} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-1)& = & 8x+\frac{5}{11} \\\Leftrightarrow & -21x+7& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{77}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+77} & = & \color{red}{88x} +5 \\\Leftrightarrow & -231x \color{red}{+77} \color{blue}{-77} \color{blue}{-88x} & = & \color{red}{88x} +5 \color{blue}{-88x} \color{blue}{-77} \\\Leftrightarrow & -231x-88x& = & 5-77 \\\Leftrightarrow & \color{red}{-319} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-319} & & \\\Leftrightarrow & x = \frac{72}{319} & & \\ & V = \left\{ \frac{72}{319} \right\} & \\\end{align}\)
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