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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -168x+35x& = & 6+30 \\\Leftrightarrow & \color{red}{-133} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-133} & & \\\Leftrightarrow & x = \frac{-36}{133} & & \\ & V = \left\{ \frac{-36}{133} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{8})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{15}{8}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{-45} & = & \color{red}{-168x} +16 \\\Leftrightarrow & 216x \color{red}{-45} \color{blue}{+45} \color{blue}{+168x} & = & \color{red}{-168x} +16 \color{blue}{+168x} \color{blue}{+45} \\\Leftrightarrow & 216x+168x& = & 16+45 \\\Leftrightarrow & \color{red}{384} x& = & 61 \\\Leftrightarrow & x = \frac{61}{384} & & \\ & V = \left\{ \frac{61}{384} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & -12x-\frac{24}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{192}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-192} & = & \color{red}{-280x} +21 \\\Leftrightarrow & -672x \color{red}{-192} \color{blue}{+192} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{+192} \\\Leftrightarrow & -672x+280x& = & 21+192 \\\Leftrightarrow & \color{red}{-392} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-392} & & \\\Leftrightarrow & x = \frac{-213}{392} & & \\ & V = \left\{ \frac{-213}{392} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 28x+\frac{35}{4}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x+ \frac{105}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{+105} & = & \color{red}{-60x} +10 \\\Leftrightarrow & 336x \color{red}{+105} \color{blue}{-105} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{-105} \\\Leftrightarrow & 336x+60x& = & 10-105 \\\Leftrightarrow & \color{red}{396} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{396} & & \\ & V = \left\{ \frac{-95}{396} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{9})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{25}{9}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-275} & = & \color{red}{-693x} +18 \\\Leftrightarrow & -990x \color{red}{-275} \color{blue}{+275} \color{blue}{+693x} & = & \color{red}{-693x} +18 \color{blue}{+693x} \color{blue}{+275} \\\Leftrightarrow & -990x+693x& = & 18+275 \\\Leftrightarrow & \color{red}{-297} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-297} & & \\\Leftrightarrow & x = \frac{-293}{297} & & \\ & V = \left\{ \frac{-293}{297} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{8})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{9}{8}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} })& = & (\frac{-144}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{+81} & = & \color{red}{-144x} +80 \\\Leftrightarrow & 1080x \color{red}{+81} \color{blue}{-81} \color{blue}{+144x} & = & \color{red}{-144x} +80 \color{blue}{+144x} \color{blue}{-81} \\\Leftrightarrow & 1080x+144x& = & 80-81 \\\Leftrightarrow & \color{red}{1224} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1224} & & \\ & V = \left\{ \frac{-1}{1224} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -16x-\frac{16}{3}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{42x} +21 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{+32} \\\Leftrightarrow & -96x-42x& = & 21+32 \\\Leftrightarrow & \color{red}{-138} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-138} & & \\\Leftrightarrow & x = \frac{-53}{138} & & \\ & V = \left\{ \frac{-53}{138} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+6} & = & \color{red}{-28x} +4 \\\Leftrightarrow & -105x \color{red}{+6} \color{blue}{-6} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-6} \\\Leftrightarrow & -105x+28x& = & 4-6 \\\Leftrightarrow & \color{red}{-77} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-77} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+10} & = & \color{red}{-21x} +4 \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & 30x+21x& = & 4-10 \\\Leftrightarrow & \color{red}{51} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{51} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{11})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -24x-\frac{30}{11}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{-270} & = & \color{red}{-495x} +77 \\\Leftrightarrow & -2376x \color{red}{-270} \color{blue}{+270} \color{blue}{+495x} & = & \color{red}{-495x} +77 \color{blue}{+495x} \color{blue}{+270} \\\Leftrightarrow & -2376x+495x& = & 77+270 \\\Leftrightarrow & \color{red}{-1881} x& = & 347 \\\Leftrightarrow & x = \frac{347}{-1881} & & \\\Leftrightarrow & x = \frac{-347}{1881} & & \\ & V = \left\{ \frac{-347}{1881} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -24x+\frac{12}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-672}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -672x \color{red}{+48} & = & \color{red}{196x} +35 \\\Leftrightarrow & -672x \color{red}{+48} \color{blue}{-48} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-48} \\\Leftrightarrow & -672x-196x& = & 35-48 \\\Leftrightarrow & \color{red}{-868} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-868} & & \\\Leftrightarrow & x = \frac{13}{868} & & \\ & V = \left\{ \frac{13}{868} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & -3x+\frac{7}{12} \\\Leftrightarrow & 8x-\frac{12}{11}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1056}{ \color{blue}{132} }x- \frac{144}{ \color{blue}{132} })& = & (\frac{-396}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1056x \color{red}{-144} & = & \color{red}{-396x} +77 \\\Leftrightarrow & 1056x \color{red}{-144} \color{blue}{+144} \color{blue}{+396x} & = & \color{red}{-396x} +77 \color{blue}{+396x} \color{blue}{+144} \\\Leftrightarrow & 1056x+396x& = & 77+144 \\\Leftrightarrow & \color{red}{1452} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1452} & & \\ & V = \left\{ \frac{221}{1452} \right\} & \\\end{align}\)
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