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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{+12} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -126x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & -126x+98x& = & 21-12 \\\Leftrightarrow & \color{red}{-28} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-28} & & \\\Leftrightarrow & x = \frac{-9}{28} & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -16x+\frac{16}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-352}{ \color{blue}{22} }x+ \frac{32}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -352x \color{red}{+32} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -352x \color{red}{+32} \color{blue}{-32} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{-32} \\\Leftrightarrow & -352x+154x& = & 99-32 \\\Leftrightarrow & \color{red}{-198} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-198} & & \\\Leftrightarrow & x = \frac{-67}{198} & & \\ & V = \left\{ \frac{-67}{198} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -240x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{-345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-345} & & \\\Leftrightarrow & x = \frac{26}{345} & & \\ & V = \left\{ \frac{26}{345} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{+165} & = & \color{red}{-308x} +32 \\\Leftrightarrow & 440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +32 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & 440x+308x& = & 32-165 \\\Leftrightarrow & \color{red}{748} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{748} & & \\ & V = \left\{ \frac{-133}{748} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-168} & = & \color{red}{385x} +44 \\\Leftrightarrow & -924x \color{red}{-168} \color{blue}{+168} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+168} \\\Leftrightarrow & -924x-385x& = & 44+168 \\\Leftrightarrow & \color{red}{-1309} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-1309} & & \\\Leftrightarrow & x = \frac{-212}{1309} & & \\ & V = \left\{ \frac{-212}{1309} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & 9x+\frac{9}{4} \\\Leftrightarrow & 4x-\frac{8}{3}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{-32} & = & \color{red}{108x} +27 \\\Leftrightarrow & 48x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +27 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & 48x-108x& = & 27+32 \\\Leftrightarrow & \color{red}{-60} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-60} & & \\\Leftrightarrow & x = \frac{-59}{60} & & \\ & V = \left\{ \frac{-59}{60} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{8}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-88} & = & \color{red}{-99x} +18 \\\Leftrightarrow & 660x \color{red}{-88} \color{blue}{+88} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{+88} \\\Leftrightarrow & 660x+99x& = & 18+88 \\\Leftrightarrow & \color{red}{759} x& = & 106 \\\Leftrightarrow & x = \frac{106}{759} & & \\ & V = \left\{ \frac{106}{759} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{3})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{8}{3}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+24} & = & \color{red}{63x} +2 \\\Leftrightarrow & -54x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +2 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & -54x-63x& = & 2-24 \\\Leftrightarrow & \color{red}{-117} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-117} & & \\\Leftrightarrow & x = \frac{22}{117} & & \\ & V = \left\{ \frac{22}{117} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{-165x} +18 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 264x+165x& = & 18+88 \\\Leftrightarrow & \color{red}{429} x& = & 106 \\\Leftrightarrow & x = \frac{106}{429} & & \\ & V = \left\{ \frac{106}{429} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{10}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-10} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -220x \color{red}{-10} \color{blue}{+10} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+10} \\\Leftrightarrow & -220x+77x& = & 6+10 \\\Leftrightarrow & \color{red}{-143} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-143} & & \\\Leftrightarrow & x = \frac{-16}{143} & & \\ & V = \left\{ \frac{-16}{143} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{+162} & = & \color{red}{-495x} +110 \\\Leftrightarrow & -2376x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & -2376x+495x& = & 110-162 \\\Leftrightarrow & \color{red}{-1881} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-1881} & & \\\Leftrightarrow & x = \frac{52}{1881} & & \\ & V = \left\{ \frac{52}{1881} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & -6x+\frac{9}{8} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -6x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-144}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-160} & = & \color{red}{-144x} +27 \\\Leftrightarrow & 600x \color{red}{-160} \color{blue}{+160} \color{blue}{+144x} & = & \color{red}{-144x} +27 \color{blue}{+144x} \color{blue}{+160} \\\Leftrightarrow & 600x+144x& = & 27+160 \\\Leftrightarrow & \color{red}{744} x& = & 187 \\\Leftrightarrow & x = \frac{187}{744} & & \\ & V = \left\{ \frac{187}{744} \right\} & \\\end{align}\)
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