Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -10x+\frac{15}{2}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+135} & = & \color{red}{-126x} +8 \\\Leftrightarrow & -180x \color{red}{+135} \color{blue}{-135} \color{blue}{+126x} & = & \color{red}{-126x} +8 \color{blue}{+126x} \color{blue}{-135} \\\Leftrightarrow & -180x+126x& = & 8-135 \\\Leftrightarrow & \color{red}{-54} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-54} & & \\\Leftrightarrow & x = \frac{127}{54} & & \\ & V = \left\{ \frac{127}{54} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{15}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+45} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 420x \color{red}{+45} \color{blue}{-45} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-45} \\\Leftrightarrow & 420x+147x& = & 14-45 \\\Leftrightarrow & \color{red}{567} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{567} & & \\ & V = \left\{ \frac{-31}{567} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{3})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{+200} & = & \color{red}{-210x} +27 \\\Leftrightarrow & -300x \color{red}{+200} \color{blue}{-200} \color{blue}{+210x} & = & \color{red}{-210x} +27 \color{blue}{+210x} \color{blue}{-200} \\\Leftrightarrow & -300x+210x& = & 27-200 \\\Leftrightarrow & \color{red}{-90} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-90} & & \\\Leftrightarrow & x = \frac{173}{90} & & \\ & V = \left\{ \frac{173}{90} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{6})& = & 3x+\frac{5}{4} \\\Leftrightarrow & -14x+\frac{35}{6}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x+ \frac{70}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{+70} & = & \color{red}{36x} +15 \\\Leftrightarrow & -168x \color{red}{+70} \color{blue}{-70} \color{blue}{-36x} & = & \color{red}{36x} +15 \color{blue}{-36x} \color{blue}{-70} \\\Leftrightarrow & -168x-36x& = & 15-70 \\\Leftrightarrow & \color{red}{-204} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-204} & & \\\Leftrightarrow & x = \frac{55}{204} & & \\ & V = \left\{ \frac{55}{204} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+18} & = & \color{red}{55x} +5 \\\Leftrightarrow & 132x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 132x-55x& = & 5-18 \\\Leftrightarrow & \color{red}{77} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{77} & & \\ & V = \left\{ \frac{-13}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 16x-\frac{12}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-108} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 1584x \color{red}{-108} \color{blue}{+108} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+108} \\\Leftrightarrow & 1584x+495x& = & 22+108 \\\Leftrightarrow & \color{red}{2079} x& = & 130 \\\Leftrightarrow & x = \frac{130}{2079} & & \\ & V = \left\{ \frac{130}{2079} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-84} & = & \color{red}{245x} +40 \\\Leftrightarrow & 1050x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 1050x-245x& = & 40+84 \\\Leftrightarrow & \color{red}{805} x& = & 124 \\\Leftrightarrow & x = \frac{124}{805} & & \\ & V = \left\{ \frac{124}{805} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+9} & = & \color{red}{70x} +15 \\\Leftrightarrow & 90x \color{red}{+9} \color{blue}{-9} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-9} \\\Leftrightarrow & 90x-70x& = & 15-9 \\\Leftrightarrow & \color{red}{20} x& = & 6 \\\Leftrightarrow & x = \frac{6}{20} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-63x} +28 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+63x} & = & \color{red}{-63x} +28 \color{blue}{+63x} \color{blue}{+60} \\\Leftrightarrow & 420x+63x& = & 28+60 \\\Leftrightarrow & \color{red}{483} x& = & 88 \\\Leftrightarrow & x = \frac{88}{483} & & \\ & V = \left\{ \frac{88}{483} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{7})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+54} & = & \color{red}{441x} +49 \\\Leftrightarrow & -630x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +49 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & -630x-441x& = & 49-54 \\\Leftrightarrow & \color{red}{-1071} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-1071} & & \\\Leftrightarrow & x = \frac{5}{1071} & & \\ & V = \left\{ \frac{5}{1071} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{-180} & = & \color{red}{770x} +77 \\\Leftrightarrow & -2640x \color{red}{-180} \color{blue}{+180} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{+180} \\\Leftrightarrow & -2640x-770x& = & 77+180 \\\Leftrightarrow & \color{red}{-3410} x& = & 257 \\\Leftrightarrow & x = \frac{257}{-3410} & & \\\Leftrightarrow & x = \frac{-257}{3410} & & \\ & V = \left\{ \frac{-257}{3410} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{405x} +50 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{-405x} & = & \color{red}{405x} +50 \color{blue}{-405x} \color{blue}{+54} \\\Leftrightarrow & -360x-405x& = & 50+54 \\\Leftrightarrow & \color{red}{-765} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-765} & & \\\Leftrightarrow & x = \frac{-104}{765} & & \\ & V = \left\{ \frac{-104}{765} \right\} & \\\end{align}\)
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