Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{35x} +3 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -84x-35x& = & 3+12 \\\Leftrightarrow & \color{red}{-119} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-119} & & \\\Leftrightarrow & x = \frac{-15}{119} & & \\ & V = \left\{ \frac{-15}{119} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+24} & = & \color{red}{81x} +2 \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-81x} & = & \color{red}{81x} +2 \color{blue}{-81x} \color{blue}{-24} \\\Leftrightarrow & -36x-81x& = & 2-24 \\\Leftrightarrow & \color{red}{-117} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-117} & & \\\Leftrightarrow & x = \frac{22}{117} & & \\ & V = \left\{ \frac{22}{117} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{25}{6}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{-84x} +21 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{+50} \\\Leftrightarrow & 120x+84x& = & 21+50 \\\Leftrightarrow & \color{red}{204} x& = & 71 \\\Leftrightarrow & x = \frac{71}{204} & & \\ & V = \left\{ \frac{71}{204} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-315x} +18 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+28} \\\Leftrightarrow & -252x+315x& = & 18+28 \\\Leftrightarrow & \color{red}{63} x& = & 46 \\\Leftrightarrow & x = \frac{46}{63} & & \\ & V = \left\{ \frac{46}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{60x} +16 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +16 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & -144x-60x& = & 16+45 \\\Leftrightarrow & \color{red}{-204} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-204} & & \\\Leftrightarrow & x = \frac{-61}{204} & & \\ & V = \left\{ \frac{-61}{204} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -2x+\frac{7}{4} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -2x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-112} & = & \color{red}{-24x} +21 \\\Leftrightarrow & 420x \color{red}{-112} \color{blue}{+112} \color{blue}{+24x} & = & \color{red}{-24x} +21 \color{blue}{+24x} \color{blue}{+112} \\\Leftrightarrow & 420x+24x& = & 21+112 \\\Leftrightarrow & \color{red}{444} x& = & 133 \\\Leftrightarrow & x = \frac{133}{444} & & \\ & V = \left\{ \frac{133}{444} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{5})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 9x+\frac{9}{5}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+27} & = & \color{red}{120x} +40 \\\Leftrightarrow & 135x \color{red}{+27} \color{blue}{-27} \color{blue}{-120x} & = & \color{red}{120x} +40 \color{blue}{-120x} \color{blue}{-27} \\\Leftrightarrow & 135x-120x& = & 40-27 \\\Leftrightarrow & \color{red}{15} x& = & 13 \\\Leftrightarrow & x = \frac{13}{15} & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-36} & = & \color{red}{45x} +20 \\\Leftrightarrow & 240x \color{red}{-36} \color{blue}{+36} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{+36} \\\Leftrightarrow & 240x-45x& = & 20+36 \\\Leftrightarrow & \color{red}{195} x& = & 56 \\\Leftrightarrow & x = \frac{56}{195} & & \\ & V = \left\{ \frac{56}{195} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & 770x+693x& = & 42-110 \\\Leftrightarrow & \color{red}{1463} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1463} & & \\ & V = \left\{ \frac{-68}{1463} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 16x-\frac{20}{3}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{384}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 384x \color{red}{-160} & = & \color{red}{72x} +21 \\\Leftrightarrow & 384x \color{red}{-160} \color{blue}{+160} \color{blue}{-72x} & = & \color{red}{72x} +21 \color{blue}{-72x} \color{blue}{+160} \\\Leftrightarrow & 384x-72x& = & 21+160 \\\Leftrightarrow & \color{red}{312} x& = & 181 \\\Leftrightarrow & x = \frac{181}{312} & & \\ & V = \left\{ \frac{181}{312} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{-30x} +5 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{+30x} & = & \color{red}{-30x} +5 \color{blue}{+30x} \color{blue}{-16} \\\Leftrightarrow & 36x+30x& = & 5-16 \\\Leftrightarrow & \color{red}{66} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{66} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -28x-\frac{14}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{42}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-42} & = & \color{red}{-99x} +22 \\\Leftrightarrow & -924x \color{red}{-42} \color{blue}{+42} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{+42} \\\Leftrightarrow & -924x+99x& = & 22+42 \\\Leftrightarrow & \color{red}{-825} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-825} & & \\\Leftrightarrow & x = \frac{-64}{825} & & \\ & V = \left\{ \frac{-64}{825} \right\} & \\\end{align}\)
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