Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-70} & = & \color{red}{135x} +21 \\\Leftrightarrow & -525x \color{red}{-70} \color{blue}{+70} \color{blue}{-135x} & = & \color{red}{135x} +21 \color{blue}{-135x} \color{blue}{+70} \\\Leftrightarrow & -525x-135x& = & 21+70 \\\Leftrightarrow & \color{red}{-660} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-660} & & \\\Leftrightarrow & x = \frac{-91}{660} & & \\ & V = \left\{ \frac{-91}{660} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & 4x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{15}{7}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-165} & = & \color{red}{308x} +49 \\\Leftrightarrow & 1155x \color{red}{-165} \color{blue}{+165} \color{blue}{-308x} & = & \color{red}{308x} +49 \color{blue}{-308x} \color{blue}{+165} \\\Leftrightarrow & 1155x-308x& = & 49+165 \\\Leftrightarrow & \color{red}{847} x& = & 214 \\\Leftrightarrow & x = \frac{214}{847} & & \\ & V = \left\{ \frac{214}{847} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+18} & = & \color{red}{42x} +28 \\\Leftrightarrow & 189x \color{red}{+18} \color{blue}{-18} \color{blue}{-42x} & = & \color{red}{42x} +28 \color{blue}{-42x} \color{blue}{-18} \\\Leftrightarrow & 189x-42x& = & 28-18 \\\Leftrightarrow & \color{red}{147} x& = & 10 \\\Leftrightarrow & x = \frac{10}{147} & & \\ & V = \left\{ \frac{10}{147} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -15x+\frac{12}{7}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x+ \frac{120}{ \color{blue}{70} })& = & (\frac{560}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{+120} & = & \color{red}{560x} +63 \\\Leftrightarrow & -1050x \color{red}{+120} \color{blue}{-120} \color{blue}{-560x} & = & \color{red}{560x} +63 \color{blue}{-560x} \color{blue}{-120} \\\Leftrightarrow & -1050x-560x& = & 63-120 \\\Leftrightarrow & \color{red}{-1610} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-1610} & & \\\Leftrightarrow & x = \frac{57}{1610} & & \\ & V = \left\{ \frac{57}{1610} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+44} & = & \color{red}{99x} +9 \\\Leftrightarrow & 264x \color{red}{+44} \color{blue}{-44} \color{blue}{-99x} & = & \color{red}{99x} +9 \color{blue}{-99x} \color{blue}{-44} \\\Leftrightarrow & 264x-99x& = & 9-44 \\\Leftrightarrow & \color{red}{165} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{165} & & \\\Leftrightarrow & x = \frac{-7}{33} & & \\ & V = \left\{ \frac{-7}{33} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{9x} +7 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{-9x} & = & \color{red}{9x} +7 \color{blue}{-9x} \color{blue}{-20} \\\Leftrightarrow & 60x-9x& = & 7-20 \\\Leftrightarrow & \color{red}{51} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{51} & & \\ & V = \left\{ \frac{-13}{51} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{231x} +56 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{-231x} & = & \color{red}{231x} +56 \color{blue}{-231x} \color{blue}{-66} \\\Leftrightarrow & 616x-231x& = & 56-66 \\\Leftrightarrow & \color{red}{385} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{385} & & \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{10}{3}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+70} & = & \color{red}{189x} +27 \\\Leftrightarrow & 84x \color{red}{+70} \color{blue}{-70} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{-70} \\\Leftrightarrow & 84x-189x& = & 27-70 \\\Leftrightarrow & \color{red}{-105} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-105} & & \\\Leftrightarrow & x = \frac{43}{105} & & \\ & V = \left\{ \frac{43}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{6})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{35}{6}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-175} & = & \color{red}{240x} +36 \\\Leftrightarrow & 1050x \color{red}{-175} \color{blue}{+175} \color{blue}{-240x} & = & \color{red}{240x} +36 \color{blue}{-240x} \color{blue}{+175} \\\Leftrightarrow & 1050x-240x& = & 36+175 \\\Leftrightarrow & \color{red}{810} x& = & 211 \\\Leftrightarrow & x = \frac{211}{810} & & \\ & V = \left\{ \frac{211}{810} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{-16} & = & \color{red}{-126x} +15 \\\Leftrightarrow & -180x \color{red}{-16} \color{blue}{+16} \color{blue}{+126x} & = & \color{red}{-126x} +15 \color{blue}{+126x} \color{blue}{+16} \\\Leftrightarrow & -180x+126x& = & 15+16 \\\Leftrightarrow & \color{red}{-54} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-54} & & \\\Leftrightarrow & x = \frac{-31}{54} & & \\ & V = \left\{ \frac{-31}{54} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{7})& = & -3x+\frac{9}{8} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-48} & = & \color{red}{-168x} +63 \\\Leftrightarrow & 560x \color{red}{-48} \color{blue}{+48} \color{blue}{+168x} & = & \color{red}{-168x} +63 \color{blue}{+168x} \color{blue}{+48} \\\Leftrightarrow & 560x+168x& = & 63+48 \\\Leftrightarrow & \color{red}{728} x& = & 111 \\\Leftrightarrow & x = \frac{111}{728} & & \\ & V = \left\{ \frac{111}{728} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{7}{12} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-672}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -672x \color{red}{+72} & = & \color{red}{756x} +49 \\\Leftrightarrow & -672x \color{red}{+72} \color{blue}{-72} \color{blue}{-756x} & = & \color{red}{756x} +49 \color{blue}{-756x} \color{blue}{-72} \\\Leftrightarrow & -672x-756x& = & 49-72 \\\Leftrightarrow & \color{red}{-1428} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-1428} & & \\\Leftrightarrow & x = \frac{23}{1428} & & \\ & V = \left\{ \frac{23}{1428} \right\} & \\\end{align}\)
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