Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-20} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -140x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & -140x+98x& = & 63+20 \\\Leftrightarrow & \color{red}{-42} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-42} & & \\\Leftrightarrow & x = \frac{-83}{42} & & \\ & V = \left\{ \frac{-83}{42} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2640}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2640x \color{red}{+180} & = & \color{red}{-770x} +77 \\\Leftrightarrow & 2640x \color{red}{+180} \color{blue}{-180} \color{blue}{+770x} & = & \color{red}{-770x} +77 \color{blue}{+770x} \color{blue}{-180} \\\Leftrightarrow & 2640x+770x& = & 77-180 \\\Leftrightarrow & \color{red}{3410} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{3410} & & \\ & V = \left\{ \frac{-103}{3410} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 18x+\frac{12}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1188}{ \color{blue}{66} }x+ \frac{72}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1188x \color{red}{+72} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 1188x \color{red}{+72} \color{blue}{-72} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-72} \\\Leftrightarrow & 1188x+330x& = & 55-72 \\\Leftrightarrow & \color{red}{1518} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{1518} & & \\ & V = \left\{ \frac{-17}{1518} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{231x} +22 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & -990x-231x& = & 22+54 \\\Leftrightarrow & \color{red}{-1221} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-1221} & & \\\Leftrightarrow & x = \frac{-76}{1221} & & \\ & V = \left\{ \frac{-76}{1221} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-352}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -352x \color{red}{-24} & = & \color{red}{-154x} +55 \\\Leftrightarrow & -352x \color{red}{-24} \color{blue}{+24} \color{blue}{+154x} & = & \color{red}{-154x} +55 \color{blue}{+154x} \color{blue}{+24} \\\Leftrightarrow & -352x+154x& = & 55+24 \\\Leftrightarrow & \color{red}{-198} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-198} & & \\\Leftrightarrow & x = \frac{-79}{198} & & \\ & V = \left\{ \frac{-79}{198} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 15-24 \\\Leftrightarrow & \color{red}{-70} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-70} & & \\\Leftrightarrow & x = \frac{9}{70} & & \\ & V = \left\{ \frac{9}{70} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{-27x} +2 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & -105x+27x& = & 2+14 \\\Leftrightarrow & \color{red}{-78} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-78} & & \\\Leftrightarrow & x = \frac{-8}{39} & & \\ & V = \left\{ \frac{-8}{39} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 28x+\frac{7}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+49} & = & \color{red}{189x} +6 \\\Leftrightarrow & 588x \color{red}{+49} \color{blue}{-49} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{-49} \\\Leftrightarrow & 588x-189x& = & 6-49 \\\Leftrightarrow & \color{red}{399} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{399} & & \\ & V = \left\{ \frac{-43}{399} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{18}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{105x} +28 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-54} \\\Leftrightarrow & 504x-105x& = & 28-54 \\\Leftrightarrow & \color{red}{399} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{399} & & \\ & V = \left\{ \frac{-26}{399} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-108} & = & \color{red}{-225x} +35 \\\Leftrightarrow & -540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & -540x+225x& = & 35+108 \\\Leftrightarrow & \color{red}{-315} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-315} & & \\\Leftrightarrow & x = \frac{-143}{315} & & \\ & V = \left\{ \frac{-143}{315} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -315x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -315x-175x& = & 15-84 \\\Leftrightarrow & \color{red}{-490} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-490} & & \\\Leftrightarrow & x = \frac{69}{490} & & \\ & V = \left\{ \frac{69}{490} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{11})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 10x+\frac{8}{11}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+72} & = & \color{red}{297x} +22 \\\Leftrightarrow & 990x \color{red}{+72} \color{blue}{-72} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{-72} \\\Leftrightarrow & 990x-297x& = & 22-72 \\\Leftrightarrow & \color{red}{693} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{693} & & \\ & V = \left\{ \frac{-50}{693} \right\} & \\\end{align}\)
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