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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+135} & = & \color{red}{252x} +40 \\\Leftrightarrow & -216x \color{red}{+135} \color{blue}{-135} \color{blue}{-252x} & = & \color{red}{252x} +40 \color{blue}{-252x} \color{blue}{-135} \\\Leftrightarrow & -216x-252x& = & 40-135 \\\Leftrightarrow & \color{red}{-468} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-468} & & \\\Leftrightarrow & x = \frac{95}{468} & & \\ & V = \left\{ \frac{95}{468} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{7})& = & -8x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{9}{7}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+9} & = & \color{red}{-56x} +8 \\\Leftrightarrow & -105x \color{red}{+9} \color{blue}{-9} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{-9} \\\Leftrightarrow & -105x+56x& = & 8-9 \\\Leftrightarrow & \color{red}{-49} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-49} & & \\\Leftrightarrow & x = \frac{1}{49} & & \\ & V = \left\{ \frac{1}{49} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{25}{12}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{-25} & = & \color{red}{-84x} +8 \\\Leftrightarrow & -300x \color{red}{-25} \color{blue}{+25} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{+25} \\\Leftrightarrow & -300x+84x& = & 8+25 \\\Leftrightarrow & \color{red}{-216} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-216} & & \\\Leftrightarrow & x = \frac{-11}{72} & & \\ & V = \left\{ \frac{-11}{72} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{-81x} +24 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{+81x} & = & \color{red}{-81x} +24 \color{blue}{+81x} \color{blue}{+8} \\\Leftrightarrow & 72x+81x& = & 24+8 \\\Leftrightarrow & \color{red}{153} x& = & 32 \\\Leftrightarrow & x = \frac{32}{153} & & \\ & V = \left\{ \frac{32}{153} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{16}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{32}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+32} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+32} \color{blue}{-32} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-32} \\\Leftrightarrow & 120x-50x& = & 45-32 \\\Leftrightarrow & \color{red}{70} x& = & 13 \\\Leftrightarrow & x = \frac{13}{70} & & \\ & V = \left\{ \frac{13}{70} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{+16} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 24x+54x& = & 27-16 \\\Leftrightarrow & \color{red}{78} x& = & 11 \\\Leftrightarrow & x = \frac{11}{78} & & \\ & V = \left\{ \frac{11}{78} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{5})& = & -8x+\frac{5}{6} \\\Leftrightarrow & -28x+\frac{28}{5}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-840}{ \color{blue}{30} }x+ \frac{168}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{-240x} +25 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{+240x} & = & \color{red}{-240x} +25 \color{blue}{+240x} \color{blue}{-168} \\\Leftrightarrow & -840x+240x& = & 25-168 \\\Leftrightarrow & \color{red}{-600} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{-600} & & \\\Leftrightarrow & x = \frac{143}{600} & & \\ & V = \left\{ \frac{143}{600} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-336}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -336x \color{red}{-60} & = & \color{red}{98x} +63 \\\Leftrightarrow & -336x \color{red}{-60} \color{blue}{+60} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+60} \\\Leftrightarrow & -336x-98x& = & 63+60 \\\Leftrightarrow & \color{red}{-434} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-434} & & \\\Leftrightarrow & x = \frac{-123}{434} & & \\ & V = \left\{ \frac{-123}{434} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{9})& = & -8x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{28}{9}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{+308} & = & \color{red}{-792x} +54 \\\Leftrightarrow & 3465x \color{red}{+308} \color{blue}{-308} \color{blue}{+792x} & = & \color{red}{-792x} +54 \color{blue}{+792x} \color{blue}{-308} \\\Leftrightarrow & 3465x+792x& = & 54-308 \\\Leftrightarrow & \color{red}{4257} x& = & -254 \\\Leftrightarrow & x = \frac{-254}{4257} & & \\ & V = \left\{ \frac{-254}{4257} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+63} & = & \color{red}{-48x} +4 \\\Leftrightarrow & 126x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +4 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 126x+48x& = & 4-63 \\\Leftrightarrow & \color{red}{174} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{174} & & \\ & V = \left\{ \frac{-59}{174} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{18}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-198} & = & \color{red}{385x} +42 \\\Leftrightarrow & -924x \color{red}{-198} \color{blue}{+198} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+198} \\\Leftrightarrow & -924x-385x& = & 42+198 \\\Leftrightarrow & \color{red}{-1309} x& = & 240 \\\Leftrightarrow & x = \frac{240}{-1309} & & \\\Leftrightarrow & x = \frac{-240}{1309} & & \\ & V = \left\{ \frac{-240}{1309} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{-16} & = & \color{red}{154x} +55 \\\Leftrightarrow & -132x \color{red}{-16} \color{blue}{+16} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+16} \\\Leftrightarrow & -132x-154x& = & 55+16 \\\Leftrightarrow & \color{red}{-286} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-286} & & \\\Leftrightarrow & x = \frac{-71}{286} & & \\ & V = \left\{ \frac{-71}{286} \right\} & \\\end{align}\)
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