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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{9})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+8} & = & \color{red}{63x} +2 \\\Leftrightarrow & -144x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +2 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & -144x-63x& = & 2-8 \\\Leftrightarrow & \color{red}{-207} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-207} & & \\\Leftrightarrow & x = \frac{2}{69} & & \\ & V = \left\{ \frac{2}{69} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-140x} +42 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+140x} & = & \color{red}{-140x} +42 \color{blue}{+140x} \color{blue}{+150} \\\Leftrightarrow & -630x+140x& = & 42+150 \\\Leftrightarrow & \color{red}{-490} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-490} & & \\\Leftrightarrow & x = \frac{-96}{245} & & \\ & V = \left\{ \frac{-96}{245} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & 378x+147x& = & 14+90 \\\Leftrightarrow & \color{red}{525} x& = & 104 \\\Leftrightarrow & x = \frac{104}{525} & & \\ & V = \left\{ \frac{104}{525} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{135x} +40 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & 300x-135x& = & 40-36 \\\Leftrightarrow & \color{red}{165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{165} & & \\ & V = \left\{ \frac{4}{165} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & 6x+\frac{3}{4} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 6x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{-112} & = & \color{red}{72x} +9 \\\Leftrightarrow & -336x \color{red}{-112} \color{blue}{+112} \color{blue}{-72x} & = & \color{red}{72x} +9 \color{blue}{-72x} \color{blue}{+112} \\\Leftrightarrow & -336x-72x& = & 9+112 \\\Leftrightarrow & \color{red}{-408} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-408} & & \\\Leftrightarrow & x = \frac{-121}{408} & & \\ & V = \left\{ \frac{-121}{408} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{56}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-56} \\\Leftrightarrow & 84x+30x& = & 9-56 \\\Leftrightarrow & \color{red}{114} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{114} & & \\ & V = \left\{ \frac{-47}{114} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{15}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-60} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 440x \color{red}{-60} \color{blue}{+60} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+60} \\\Leftrightarrow & 440x+308x& = & 99+60 \\\Leftrightarrow & \color{red}{748} x& = & 159 \\\Leftrightarrow & x = \frac{159}{748} & & \\ & V = \left\{ \frac{159}{748} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -396x+165x& = & 44+54 \\\Leftrightarrow & \color{red}{-231} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-231} & & \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -24x-\frac{24}{5}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-264} & = & \color{red}{-275x} +40 \\\Leftrightarrow & -1320x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +40 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & -1320x+275x& = & 40+264 \\\Leftrightarrow & \color{red}{-1045} x& = & 304 \\\Leftrightarrow & x = \frac{304}{-1045} & & \\\Leftrightarrow & x = \frac{-16}{55} & & \\ & V = \left\{ \frac{-16}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -4x+\frac{9}{7} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{-112x} +36 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +36 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & 700x+112x& = & 36+105 \\\Leftrightarrow & \color{red}{812} x& = & 141 \\\Leftrightarrow & x = \frac{141}{812} & & \\ & V = \left\{ \frac{141}{812} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & -270x+105x& = & 40+54 \\\Leftrightarrow & \color{red}{-165} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-165} & & \\\Leftrightarrow & x = \frac{-94}{165} & & \\ & V = \left\{ \frac{-94}{165} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x-\frac{6}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{-24} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 528x \color{red}{-24} \color{blue}{+24} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{+24} \\\Leftrightarrow & 528x+220x& = & 33+24 \\\Leftrightarrow & \color{red}{748} x& = & 57 \\\Leftrightarrow & x = \frac{57}{748} & & \\ & V = \left\{ \frac{57}{748} \right\} & \\\end{align}\)
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