Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-75} & = & \color{red}{220x} +66 \\\Leftrightarrow & -825x \color{red}{-75} \color{blue}{+75} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{+75} \\\Leftrightarrow & -825x-220x& = & 66+75 \\\Leftrightarrow & \color{red}{-1045} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-1045} & & \\\Leftrightarrow & x = \frac{-141}{1045} & & \\ & V = \left\{ \frac{-141}{1045} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-105x} +24 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & -252x+105x& = & 24+56 \\\Leftrightarrow & \color{red}{-147} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-147} & & \\\Leftrightarrow & x = \frac{-80}{147} & & \\ & V = \left\{ \frac{-80}{147} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{180}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+180} & = & \color{red}{297x} +88 \\\Leftrightarrow & 1980x \color{red}{+180} \color{blue}{-180} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{-180} \\\Leftrightarrow & 1980x-297x& = & 88-180 \\\Leftrightarrow & \color{red}{1683} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{1683} & & \\ & V = \left\{ \frac{-92}{1683} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{2})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 28x-\frac{21}{2}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{56}{ \color{blue}{2} }x- \frac{21}{ \color{blue}{2} })& = & (\frac{6}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 56x \color{red}{-21} & = & \color{red}{6x} +5 \\\Leftrightarrow & 56x \color{red}{-21} \color{blue}{+21} \color{blue}{-6x} & = & \color{red}{6x} +5 \color{blue}{-6x} \color{blue}{+21} \\\Leftrightarrow & 56x-6x& = & 5+21 \\\Leftrightarrow & \color{red}{50} x& = & 26 \\\Leftrightarrow & x = \frac{26}{50} & & \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{2100}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 2100x \color{red}{+300} & = & \color{red}{490x} +63 \\\Leftrightarrow & 2100x \color{red}{+300} \color{blue}{-300} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-300} \\\Leftrightarrow & 2100x-490x& = & 63-300 \\\Leftrightarrow & \color{red}{1610} x& = & -237 \\\Leftrightarrow & x = \frac{-237}{1610} & & \\ & V = \left\{ \frac{-237}{1610} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 9x+\frac{15}{8}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+15} & = & \color{red}{-32x} +28 \\\Leftrightarrow & 72x \color{red}{+15} \color{blue}{-15} \color{blue}{+32x} & = & \color{red}{-32x} +28 \color{blue}{+32x} \color{blue}{-15} \\\Leftrightarrow & 72x+32x& = & 28-15 \\\Leftrightarrow & \color{red}{104} x& = & 13 \\\Leftrightarrow & x = \frac{13}{104} & & \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 6x+\frac{3}{5} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 6x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-70} & = & \color{red}{90x} +9 \\\Leftrightarrow & -525x \color{red}{-70} \color{blue}{+70} \color{blue}{-90x} & = & \color{red}{90x} +9 \color{blue}{-90x} \color{blue}{+70} \\\Leftrightarrow & -525x-90x& = & 9+70 \\\Leftrightarrow & \color{red}{-615} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-615} & & \\\Leftrightarrow & x = \frac{-79}{615} & & \\ & V = \left\{ \frac{-79}{615} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +9 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 9-6 \\\Leftrightarrow & \color{red}{-119} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-119} & & \\\Leftrightarrow & x = \frac{-3}{119} & & \\ & V = \left\{ \frac{-3}{119} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -8x+\frac{9}{8} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1320}{ \color{blue}{88} }x- \frac{120}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1320x \color{red}{-120} & = & \color{red}{-704x} +99 \\\Leftrightarrow & -1320x \color{red}{-120} \color{blue}{+120} \color{blue}{+704x} & = & \color{red}{-704x} +99 \color{blue}{+704x} \color{blue}{+120} \\\Leftrightarrow & -1320x+704x& = & 99+120 \\\Leftrightarrow & \color{red}{-616} x& = & 219 \\\Leftrightarrow & x = \frac{219}{-616} & & \\\Leftrightarrow & x = \frac{-219}{616} & & \\ & V = \left\{ \frac{-219}{616} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{10}{3}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+110} & = & \color{red}{-231x} +6 \\\Leftrightarrow & -198x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +6 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & -198x+231x& = & 6-110 \\\Leftrightarrow & \color{red}{33} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{33} & & \\ & V = \left\{ \frac{-104}{33} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{7})& = & -2x+\frac{5}{3} \\\Leftrightarrow & 21x-4& = & -2x+\frac{5}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{12}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-12} & = & \color{red}{-6x} +5 \\\Leftrightarrow & 63x \color{red}{-12} \color{blue}{+12} \color{blue}{+6x} & = & \color{red}{-6x} +5 \color{blue}{+6x} \color{blue}{+12} \\\Leftrightarrow & 63x+6x& = & 5+12 \\\Leftrightarrow & \color{red}{69} x& = & 17 \\\Leftrightarrow & x = \frac{17}{69} & & \\ & V = \left\{ \frac{17}{69} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+6} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -30x+35x& = & 6-6 \\\Leftrightarrow & \color{red}{5} x& = & 0 \\\Leftrightarrow & x = \frac{0}{5} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
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