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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-220} & = & \color{red}{385x} +35 \\\Leftrightarrow & -924x \color{red}{-220} \color{blue}{+220} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{+220} \\\Leftrightarrow & -924x-385x& = & 35+220 \\\Leftrightarrow & \color{red}{-1309} x& = & 255 \\\Leftrightarrow & x = \frac{255}{-1309} & & \\\Leftrightarrow & x = \frac{-15}{77} & & \\ & V = \left\{ \frac{-15}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{9})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{8}{9}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-8} & = & \color{red}{-81x} +8 \\\Leftrightarrow & 90x \color{red}{-8} \color{blue}{+8} \color{blue}{+81x} & = & \color{red}{-81x} +8 \color{blue}{+81x} \color{blue}{+8} \\\Leftrightarrow & 90x+81x& = & 8+8 \\\Leftrightarrow & \color{red}{171} x& = & 16 \\\Leftrightarrow & x = \frac{16}{171} & & \\ & V = \left\{ \frac{16}{171} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{2})& = & 8x+\frac{3}{7} \\\Leftrightarrow & -21x+\frac{21}{2}& = & 8x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-294}{ \color{blue}{14} }x+ \frac{147}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -294x \color{red}{+147} & = & \color{red}{112x} +6 \\\Leftrightarrow & -294x \color{red}{+147} \color{blue}{-147} \color{blue}{-112x} & = & \color{red}{112x} +6 \color{blue}{-112x} \color{blue}{-147} \\\Leftrightarrow & -294x-112x& = & 6-147 \\\Leftrightarrow & \color{red}{-406} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-406} & & \\\Leftrightarrow & x = \frac{141}{406} & & \\ & V = \left\{ \frac{141}{406} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{-105x} +28 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-60} \\\Leftrightarrow & 252x+105x& = & 28-60 \\\Leftrightarrow & \color{red}{357} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{357} & & \\ & V = \left\{ \frac{-32}{357} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & 2x+\frac{5}{2} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 2x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{44x} +55 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{-44x} & = & \color{red}{44x} +55 \color{blue}{-44x} \color{blue}{+30} \\\Leftrightarrow & 330x-44x& = & 55+30 \\\Leftrightarrow & \color{red}{286} x& = & 85 \\\Leftrightarrow & x = \frac{85}{286} & & \\ & V = \left\{ \frac{85}{286} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & -8x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{35}{3}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-175} & = & \color{red}{-120x} +6 \\\Leftrightarrow & 315x \color{red}{-175} \color{blue}{+175} \color{blue}{+120x} & = & \color{red}{-120x} +6 \color{blue}{+120x} \color{blue}{+175} \\\Leftrightarrow & 315x+120x& = & 6+175 \\\Leftrightarrow & \color{red}{435} x& = & 181 \\\Leftrightarrow & x = \frac{181}{435} & & \\ & V = \left\{ \frac{181}{435} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & 6x+\frac{7}{4} \\\Leftrightarrow & -28x+\frac{21}{11}& = & 6x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{84}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+84} & = & \color{red}{264x} +77 \\\Leftrightarrow & -1232x \color{red}{+84} \color{blue}{-84} \color{blue}{-264x} & = & \color{red}{264x} +77 \color{blue}{-264x} \color{blue}{-84} \\\Leftrightarrow & -1232x-264x& = & 77-84 \\\Leftrightarrow & \color{red}{-1496} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-1496} & & \\\Leftrightarrow & x = \frac{7}{1496} & & \\ & V = \left\{ \frac{7}{1496} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-40} & = & \color{red}{-54x} +7 \\\Leftrightarrow & -150x \color{red}{-40} \color{blue}{+40} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{+40} \\\Leftrightarrow & -150x+54x& = & 7+40 \\\Leftrightarrow & \color{red}{-96} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-96} & & \\\Leftrightarrow & x = \frac{-47}{96} & & \\ & V = \left\{ \frac{-47}{96} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{9})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-4} & = & \color{red}{-81x} +15 \\\Leftrightarrow & -72x \color{red}{-4} \color{blue}{+4} \color{blue}{+81x} & = & \color{red}{-81x} +15 \color{blue}{+81x} \color{blue}{+4} \\\Leftrightarrow & -72x+81x& = & 15+4 \\\Leftrightarrow & \color{red}{9} x& = & 19 \\\Leftrightarrow & x = \frac{19}{9} & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{15}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+135} & = & \color{red}{-441x} +56 \\\Leftrightarrow & -630x \color{red}{+135} \color{blue}{-135} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{-135} \\\Leftrightarrow & -630x+441x& = & 56-135 \\\Leftrightarrow & \color{red}{-189} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-189} & & \\\Leftrightarrow & x = \frac{79}{189} & & \\ & V = \left\{ \frac{79}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{9})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{4}{9}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{+16} & = & \color{red}{-180x} +81 \\\Leftrightarrow & 216x \color{red}{+16} \color{blue}{-16} \color{blue}{+180x} & = & \color{red}{-180x} +81 \color{blue}{+180x} \color{blue}{-16} \\\Leftrightarrow & 216x+180x& = & 81-16 \\\Leftrightarrow & \color{red}{396} x& = & 65 \\\Leftrightarrow & x = \frac{65}{396} & & \\ & V = \left\{ \frac{65}{396} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{25}{6}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{126x} +60 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{-126x} & = & \color{red}{126x} +60 \color{blue}{-126x} \color{blue}{-175} \\\Leftrightarrow & 420x-126x& = & 60-175 \\\Leftrightarrow & \color{red}{294} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{294} & & \\ & V = \left\{ \frac{-115}{294} \right\} & \\\end{align}\)
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