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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-8} & = & \color{red}{-33x} +6 \\\Leftrightarrow & 88x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & 88x+33x& = & 6+8 \\\Leftrightarrow & \color{red}{121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{121} & & \\ & V = \left\{ \frac{14}{121} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 35x-\frac{21}{11}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{189}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-189} & = & \color{red}{-792x} +22 \\\Leftrightarrow & 3465x \color{red}{-189} \color{blue}{+189} \color{blue}{+792x} & = & \color{red}{-792x} +22 \color{blue}{+792x} \color{blue}{+189} \\\Leftrightarrow & 3465x+792x& = & 22+189 \\\Leftrightarrow & \color{red}{4257} x& = & 211 \\\Leftrightarrow & x = \frac{211}{4257} & & \\ & V = \left\{ \frac{211}{4257} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{4})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{9}{4}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x- \frac{45}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{-45} & = & \color{red}{100x} +18 \\\Leftrightarrow & 120x \color{red}{-45} \color{blue}{+45} \color{blue}{-100x} & = & \color{red}{100x} +18 \color{blue}{-100x} \color{blue}{+45} \\\Leftrightarrow & 120x-100x& = & 18+45 \\\Leftrightarrow & \color{red}{20} x& = & 63 \\\Leftrightarrow & x = \frac{63}{20} & & \\ & V = \left\{ \frac{63}{20} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -210x+147x& = & 56+18 \\\Leftrightarrow & \color{red}{-63} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-63} & & \\\Leftrightarrow & x = \frac{-74}{63} & & \\ & V = \left\{ \frac{-74}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+16} & = & \color{red}{63x} +3 \\\Leftrightarrow & -56x \color{red}{+16} \color{blue}{-16} \color{blue}{-63x} & = & \color{red}{63x} +3 \color{blue}{-63x} \color{blue}{-16} \\\Leftrightarrow & -56x-63x& = & 3-16 \\\Leftrightarrow & \color{red}{-119} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-119} & & \\\Leftrightarrow & x = \frac{13}{119} & & \\ & V = \left\{ \frac{13}{119} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -9x+\frac{9}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+9} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -63x \color{red}{+9} \color{blue}{-9} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-9} \\\Leftrightarrow & -63x+35x& = & 8-9 \\\Leftrightarrow & \color{red}{-28} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-28} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-44} & = & \color{red}{693x} +54 \\\Leftrightarrow & -594x \color{red}{-44} \color{blue}{+44} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+44} \\\Leftrightarrow & -594x-693x& = & 54+44 \\\Leftrightarrow & \color{red}{-1287} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-1287} & & \\\Leftrightarrow & x = \frac{-98}{1287} & & \\ & V = \left\{ \frac{-98}{1287} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+84} & = & \color{red}{539x} +88 \\\Leftrightarrow & 924x \color{red}{+84} \color{blue}{-84} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-84} \\\Leftrightarrow & 924x-539x& = & 88-84 \\\Leftrightarrow & \color{red}{385} x& = & 4 \\\Leftrightarrow & x = \frac{4}{385} & & \\ & V = \left\{ \frac{4}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-72} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 180x \color{red}{-72} \color{blue}{+72} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{+72} \\\Leftrightarrow & 180x+150x& = & 25+72 \\\Leftrightarrow & \color{red}{330} x& = & 97 \\\Leftrightarrow & x = \frac{97}{330} & & \\ & V = \left\{ \frac{97}{330} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & -6x+\frac{3}{7} \\\Leftrightarrow & -35x-\frac{21}{11}& = & -6x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{-147} & = & \color{red}{-462x} +33 \\\Leftrightarrow & -2695x \color{red}{-147} \color{blue}{+147} \color{blue}{+462x} & = & \color{red}{-462x} +33 \color{blue}{+462x} \color{blue}{+147} \\\Leftrightarrow & -2695x+462x& = & 33+147 \\\Leftrightarrow & \color{red}{-2233} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-2233} & & \\\Leftrightarrow & x = \frac{-180}{2233} & & \\ & V = \left\{ \frac{-180}{2233} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{8})& = & -8x+\frac{3}{11} \\\Leftrightarrow & -25x-\frac{15}{8}& = & -8x+\frac{3}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{24}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{-165} & = & \color{red}{-704x} +24 \\\Leftrightarrow & -2200x \color{red}{-165} \color{blue}{+165} \color{blue}{+704x} & = & \color{red}{-704x} +24 \color{blue}{+704x} \color{blue}{+165} \\\Leftrightarrow & -2200x+704x& = & 24+165 \\\Leftrightarrow & \color{red}{-1496} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-1496} & & \\\Leftrightarrow & x = \frac{-189}{1496} & & \\ & V = \left\{ \frac{-189}{1496} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+50} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -550x \color{red}{+50} \color{blue}{-50} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-50} \\\Leftrightarrow & -550x+385x& = & 22-50 \\\Leftrightarrow & \color{red}{-165} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-165} & & \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)
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