Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{11})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{+35} & = & \color{red}{33x} +5 \\\Leftrightarrow & -385x \color{red}{+35} \color{blue}{-35} \color{blue}{-33x} & = & \color{red}{33x} +5 \color{blue}{-33x} \color{blue}{-35} \\\Leftrightarrow & -385x-33x& = & 5-35 \\\Leftrightarrow & \color{red}{-418} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{-418} & & \\\Leftrightarrow & x = \frac{15}{209} & & \\ & V = \left\{ \frac{15}{209} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x+\frac{30}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+30} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 132x \color{red}{+30} \color{blue}{-30} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-30} \\\Leftrightarrow & 132x+55x& = & 5-30 \\\Leftrightarrow & \color{red}{187} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{187} & & \\ & V = \left\{ \frac{-25}{187} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{3})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 20x-\frac{8}{3}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-56} & = & \color{red}{-147x} +15 \\\Leftrightarrow & 420x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +15 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & 420x+147x& = & 15+56 \\\Leftrightarrow & \color{red}{567} x& = & 71 \\\Leftrightarrow & x = \frac{71}{567} & & \\ & V = \left\{ \frac{71}{567} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-200} & = & \color{red}{210x} +9 \\\Leftrightarrow & 600x \color{red}{-200} \color{blue}{+200} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{+200} \\\Leftrightarrow & 600x-210x& = & 9+200 \\\Leftrightarrow & \color{red}{390} x& = & 209 \\\Leftrightarrow & x = \frac{209}{390} & & \\ & V = \left\{ \frac{209}{390} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{35}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+35} & = & \color{red}{27x} +10 \\\Leftrightarrow & -84x \color{red}{+35} \color{blue}{-35} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-35} \\\Leftrightarrow & -84x-27x& = & 10-35 \\\Leftrightarrow & \color{red}{-111} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-111} & & \\\Leftrightarrow & x = \frac{25}{111} & & \\ & V = \left\{ \frac{25}{111} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{8})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 25x-\frac{15}{8}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2200}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2200x \color{red}{-165} & = & \color{red}{264x} +16 \\\Leftrightarrow & 2200x \color{red}{-165} \color{blue}{+165} \color{blue}{-264x} & = & \color{red}{264x} +16 \color{blue}{-264x} \color{blue}{+165} \\\Leftrightarrow & 2200x-264x& = & 16+165 \\\Leftrightarrow & \color{red}{1936} x& = & 181 \\\Leftrightarrow & x = \frac{181}{1936} & & \\ & V = \left\{ \frac{181}{1936} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 28+66 \\\Leftrightarrow & \color{red}{77} x& = & 94 \\\Leftrightarrow & x = \frac{94}{77} & & \\ & V = \left\{ \frac{94}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & -8x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{28}{11}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{+196} & = & \color{red}{-616x} +110 \\\Leftrightarrow & 2695x \color{red}{+196} \color{blue}{-196} \color{blue}{+616x} & = & \color{red}{-616x} +110 \color{blue}{+616x} \color{blue}{-196} \\\Leftrightarrow & 2695x+616x& = & 110-196 \\\Leftrightarrow & \color{red}{3311} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{3311} & & \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{6})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -14x-\frac{35}{6}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-924}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{198}{ \color{blue}{66} }x+ \frac{30}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -924x \color{red}{-385} & = & \color{red}{198x} +30 \\\Leftrightarrow & -924x \color{red}{-385} \color{blue}{+385} \color{blue}{-198x} & = & \color{red}{198x} +30 \color{blue}{-198x} \color{blue}{+385} \\\Leftrightarrow & -924x-198x& = & 30+385 \\\Leftrightarrow & \color{red}{-1122} x& = & 415 \\\Leftrightarrow & x = \frac{415}{-1122} & & \\\Leftrightarrow & x = \frac{-415}{1122} & & \\ & V = \left\{ \frac{-415}{1122} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{275x} +30 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 1320x-275x& = & 30+132 \\\Leftrightarrow & \color{red}{1045} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1045} & & \\ & V = \left\{ \frac{162}{1045} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{-42x} +70 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{+42x} & = & \color{red}{-42x} +70 \color{blue}{+42x} \color{blue}{+18} \\\Leftrightarrow & 315x+42x& = & 70+18 \\\Leftrightarrow & \color{red}{357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{357} & & \\ & V = \left\{ \frac{88}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-20} & = & \color{red}{42x} +49 \\\Leftrightarrow & 280x \color{red}{-20} \color{blue}{+20} \color{blue}{-42x} & = & \color{red}{42x} +49 \color{blue}{-42x} \color{blue}{+20} \\\Leftrightarrow & 280x-42x& = & 49+20 \\\Leftrightarrow & \color{red}{238} x& = & 69 \\\Leftrightarrow & x = \frac{69}{238} & & \\ & V = \left\{ \frac{69}{238} \right\} & \\\end{align}\)
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