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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{-20} & = & \color{red}{126x} +21 \\\Leftrightarrow & -56x \color{red}{-20} \color{blue}{+20} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{+20} \\\Leftrightarrow & -56x-126x& = & 21+20 \\\Leftrightarrow & \color{red}{-182} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-182} & & \\\Leftrightarrow & x = \frac{-41}{182} & & \\ & V = \left\{ \frac{-41}{182} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-6} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 70x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & 70x+49x& = & 10+6 \\\Leftrightarrow & \color{red}{119} x& = & 16 \\\Leftrightarrow & x = \frac{16}{119} & & \\ & V = \left\{ \frac{16}{119} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{7})& = & -8x+\frac{9}{5} \\\Leftrightarrow & -15x-\frac{20}{7}& = & -8x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-100} & = & \color{red}{-280x} +63 \\\Leftrightarrow & -525x \color{red}{-100} \color{blue}{+100} \color{blue}{+280x} & = & \color{red}{-280x} +63 \color{blue}{+280x} \color{blue}{+100} \\\Leftrightarrow & -525x+280x& = & 63+100 \\\Leftrightarrow & \color{red}{-245} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-245} & & \\\Leftrightarrow & x = \frac{-163}{245} & & \\ & V = \left\{ \frac{-163}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{9}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x- \frac{81}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{-81} & = & \color{red}{315x} +14 \\\Leftrightarrow & -567x \color{red}{-81} \color{blue}{+81} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{+81} \\\Leftrightarrow & -567x-315x& = & 14+81 \\\Leftrightarrow & \color{red}{-882} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-882} & & \\\Leftrightarrow & x = \frac{-95}{882} & & \\ & V = \left\{ \frac{-95}{882} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{4})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -28x-\frac{21}{4}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-784}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -784x \color{red}{-147} & = & \color{red}{140x} +8 \\\Leftrightarrow & -784x \color{red}{-147} \color{blue}{+147} \color{blue}{-140x} & = & \color{red}{140x} +8 \color{blue}{-140x} \color{blue}{+147} \\\Leftrightarrow & -784x-140x& = & 8+147 \\\Leftrightarrow & \color{red}{-924} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-924} & & \\\Leftrightarrow & x = \frac{-155}{924} & & \\ & V = \left\{ \frac{-155}{924} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{175x} +45 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 210x-175x& = & 45-84 \\\Leftrightarrow & \color{red}{35} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{35} & & \\ & V = \left\{ \frac{-39}{35} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{8})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 10x-\frac{15}{8}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{400}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 400x \color{red}{-75} & = & \color{red}{360x} +36 \\\Leftrightarrow & 400x \color{red}{-75} \color{blue}{+75} \color{blue}{-360x} & = & \color{red}{360x} +36 \color{blue}{-360x} \color{blue}{+75} \\\Leftrightarrow & 400x-360x& = & 36+75 \\\Leftrightarrow & \color{red}{40} x& = & 111 \\\Leftrightarrow & x = \frac{111}{40} & & \\ & V = \left\{ \frac{111}{40} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{15}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-45} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -330x \color{red}{-45} \color{blue}{+45} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+45} \\\Leftrightarrow & -330x+231x& = & 44+45 \\\Leftrightarrow & \color{red}{-99} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-99} & & \\\Leftrightarrow & x = \frac{-89}{99} & & \\ & V = \left\{ \frac{-89}{99} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-25x} +3 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +3 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 120x+25x& = & 3-24 \\\Leftrightarrow & \color{red}{145} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{145} & & \\ & V = \left\{ \frac{-21}{145} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{66x} +18 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +18 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 693x-66x& = & 18+154 \\\Leftrightarrow & \color{red}{627} x& = & 172 \\\Leftrightarrow & x = \frac{172}{627} & & \\ & V = \left\{ \frac{172}{627} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -6x-\frac{8}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-8} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -42x \color{red}{-8} \color{blue}{+8} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+8} \\\Leftrightarrow & -42x+49x& = & 9+8 \\\Leftrightarrow & \color{red}{7} x& = & 17 \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{20}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-20} & = & \color{red}{385x} +66 \\\Leftrightarrow & 330x \color{red}{-20} \color{blue}{+20} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+20} \\\Leftrightarrow & 330x-385x& = & 66+20 \\\Leftrightarrow & \color{red}{-55} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-55} & & \\\Leftrightarrow & x = \frac{-86}{55} & & \\ & V = \left\{ \frac{-86}{55} \right\} & \\\end{align}\)
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