Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+8} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 80x \color{red}{+8} \color{blue}{-8} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-8} \\\Leftrightarrow & 80x+50x& = & 15-8 \\\Leftrightarrow & \color{red}{130} x& = & 7 \\\Leftrightarrow & x = \frac{7}{130} & & \\ & V = \left\{ \frac{7}{130} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & -2x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-72}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+135} & = & \color{red}{-72x} +32 \\\Leftrightarrow & 540x \color{red}{+135} \color{blue}{-135} \color{blue}{+72x} & = & \color{red}{-72x} +32 \color{blue}{+72x} \color{blue}{-135} \\\Leftrightarrow & 540x+72x& = & 32-135 \\\Leftrightarrow & \color{red}{612} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{612} & & \\ & V = \left\{ \frac{-103}{612} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{10}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{+110} & = & \color{red}{693x} +54 \\\Leftrightarrow & -990x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & -990x-693x& = & 54-110 \\\Leftrightarrow & \color{red}{-1683} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-1683} & & \\\Leftrightarrow & x = \frac{56}{1683} & & \\ & V = \left\{ \frac{56}{1683} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x- \frac{105}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{-105} & = & \color{red}{-275x} +88 \\\Leftrightarrow & -770x \color{red}{-105} \color{blue}{+105} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{+105} \\\Leftrightarrow & -770x+275x& = & 88+105 \\\Leftrightarrow & \color{red}{-495} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-495} & & \\\Leftrightarrow & x = \frac{-193}{495} & & \\ & V = \left\{ \frac{-193}{495} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{70x} +3 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 60x-70x& = & 3+24 \\\Leftrightarrow & \color{red}{-10} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-10} & & \\\Leftrightarrow & x = \frac{-27}{10} & & \\ & V = \left\{ \frac{-27}{10} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+40} & = & \color{red}{385x} +66 \\\Leftrightarrow & -330x \color{red}{+40} \color{blue}{-40} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-40} \\\Leftrightarrow & -330x-385x& = & 66-40 \\\Leftrightarrow & \color{red}{-715} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-715} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 60x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{25} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{25} & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{9})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 8x+\frac{20}{9}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+140} & = & \color{red}{189x} +72 \\\Leftrightarrow & 504x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +72 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & 504x-189x& = & 72-140 \\\Leftrightarrow & \color{red}{315} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{315} & & \\ & V = \left\{ \frac{-68}{315} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{11})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x-\frac{8}{11}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-8} & = & \color{red}{-33x} +8 \\\Leftrightarrow & 220x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +8 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & 220x+33x& = & 8+8 \\\Leftrightarrow & \color{red}{253} x& = & 16 \\\Leftrightarrow & x = \frac{16}{253} & & \\ & V = \left\{ \frac{16}{253} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{7})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 4x-\frac{4}{7}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x- \frac{36}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{-36} & = & \color{red}{567x} +49 \\\Leftrightarrow & 252x \color{red}{-36} \color{blue}{+36} \color{blue}{-567x} & = & \color{red}{567x} +49 \color{blue}{-567x} \color{blue}{+36} \\\Leftrightarrow & 252x-567x& = & 49+36 \\\Leftrightarrow & \color{red}{-315} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-315} & & \\\Leftrightarrow & x = \frac{-17}{63} & & \\ & V = \left\{ \frac{-17}{63} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{9}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-27} & = & \color{red}{105x} +20 \\\Leftrightarrow & 225x \color{red}{-27} \color{blue}{+27} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+27} \\\Leftrightarrow & 225x-105x& = & 20+27 \\\Leftrightarrow & \color{red}{120} x& = & 47 \\\Leftrightarrow & x = \frac{47}{120} & & \\ & V = \left\{ \frac{47}{120} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -2x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{-108} & = & \color{red}{-90x} +50 \\\Leftrightarrow & -810x \color{red}{-108} \color{blue}{+108} \color{blue}{+90x} & = & \color{red}{-90x} +50 \color{blue}{+90x} \color{blue}{+108} \\\Leftrightarrow & -810x+90x& = & 50+108 \\\Leftrightarrow & \color{red}{-720} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-720} & & \\\Leftrightarrow & x = \frac{-79}{360} & & \\ & V = \left\{ \frac{-79}{360} \right\} & \\\end{align}\)
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