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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{60x} +20 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{-60x} & = & \color{red}{60x} +20 \color{blue}{-60x} \color{blue}{-36} \\\Leftrightarrow & 225x-60x& = & 20-36 \\\Leftrightarrow & \color{red}{165} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{165} & & \\ & V = \left\{ \frac{-16}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+12} & = & \color{red}{98x} +21 \\\Leftrightarrow & -84x \color{red}{+12} \color{blue}{-12} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{-12} \\\Leftrightarrow & -84x-98x& = & 21-12 \\\Leftrightarrow & \color{red}{-182} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-182} & & \\\Leftrightarrow & x = \frac{-9}{182} & & \\ & V = \left\{ \frac{-9}{182} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{9}{5} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+30} & = & \color{red}{-315x} +63 \\\Leftrightarrow & -280x \color{red}{+30} \color{blue}{-30} \color{blue}{+315x} & = & \color{red}{-315x} +63 \color{blue}{+315x} \color{blue}{-30} \\\Leftrightarrow & -280x+315x& = & 63-30 \\\Leftrightarrow & \color{red}{35} x& = & 33 \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -360x+105x& = & 50-36 \\\Leftrightarrow & \color{red}{-255} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-255} & & \\\Leftrightarrow & x = \frac{-14}{255} & & \\ & V = \left\{ \frac{-14}{255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{11})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{25}{11}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+75} & = & \color{red}{-132x} +88 \\\Leftrightarrow & 495x \color{red}{+75} \color{blue}{-75} \color{blue}{+132x} & = & \color{red}{-132x} +88 \color{blue}{+132x} \color{blue}{-75} \\\Leftrightarrow & 495x+132x& = & 88-75 \\\Leftrightarrow & \color{red}{627} x& = & 13 \\\Leftrightarrow & x = \frac{13}{627} & & \\ & V = \left\{ \frac{13}{627} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1344}{ \color{blue}{84} }x+ \frac{192}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1344x \color{red}{+192} & = & \color{red}{-588x} +49 \\\Leftrightarrow & 1344x \color{red}{+192} \color{blue}{-192} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{-192} \\\Leftrightarrow & 1344x+588x& = & 49-192 \\\Leftrightarrow & \color{red}{1932} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{1932} & & \\ & V = \left\{ \frac{-143}{1932} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{9})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-70} & = & \color{red}{-441x} +54 \\\Leftrightarrow & -630x \color{red}{-70} \color{blue}{+70} \color{blue}{+441x} & = & \color{red}{-441x} +54 \color{blue}{+441x} \color{blue}{+70} \\\Leftrightarrow & -630x+441x& = & 54+70 \\\Leftrightarrow & \color{red}{-189} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-189} & & \\\Leftrightarrow & x = \frac{-124}{189} & & \\ & V = \left\{ \frac{-124}{189} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +9 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 9+10 \\\Leftrightarrow & \color{red}{-119} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-119} & & \\\Leftrightarrow & x = \frac{-19}{119} & & \\ & V = \left\{ \frac{-19}{119} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{+165} & = & \color{red}{-308x} +20 \\\Leftrightarrow & 440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +20 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & 440x+308x& = & 20-165 \\\Leftrightarrow & \color{red}{748} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{748} & & \\ & V = \left\{ \frac{-145}{748} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{11})& = & 4x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{20}{11}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{40}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+40} & = & \color{red}{88x} +33 \\\Leftrightarrow & 550x \color{red}{+40} \color{blue}{-40} \color{blue}{-88x} & = & \color{red}{88x} +33 \color{blue}{-88x} \color{blue}{-40} \\\Leftrightarrow & 550x-88x& = & 33-40 \\\Leftrightarrow & \color{red}{462} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{462} & & \\\Leftrightarrow & x = \frac{-1}{66} & & \\ & V = \left\{ \frac{-1}{66} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{15}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{60}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+60} & = & \color{red}{196x} +21 \\\Leftrightarrow & 560x \color{red}{+60} \color{blue}{-60} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-60} \\\Leftrightarrow & 560x-196x& = & 21-60 \\\Leftrightarrow & \color{red}{364} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{364} & & \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-252}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -252x \color{red}{+36} & = & \color{red}{294x} +35 \\\Leftrightarrow & -252x \color{red}{+36} \color{blue}{-36} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-36} \\\Leftrightarrow & -252x-294x& = & 35-36 \\\Leftrightarrow & \color{red}{-546} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-546} & & \\\Leftrightarrow & x = \frac{1}{546} & & \\ & V = \left\{ \frac{1}{546} \right\} & \\\end{align}\)
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