Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{8})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{25}{8}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x- \frac{125}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{-125} & = & \color{red}{360x} +16 \\\Leftrightarrow & 800x \color{red}{-125} \color{blue}{+125} \color{blue}{-360x} & = & \color{red}{360x} +16 \color{blue}{-360x} \color{blue}{+125} \\\Leftrightarrow & 800x-360x& = & 16+125 \\\Leftrightarrow & \color{red}{440} x& = & 141 \\\Leftrightarrow & x = \frac{141}{440} & & \\ & V = \left\{ \frac{141}{440} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -8x+\frac{8}{5}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+16} & = & \color{red}{-90x} +9 \\\Leftrightarrow & -80x \color{red}{+16} \color{blue}{-16} \color{blue}{+90x} & = & \color{red}{-90x} +9 \color{blue}{+90x} \color{blue}{-16} \\\Leftrightarrow & -80x+90x& = & 9-16 \\\Leftrightarrow & \color{red}{10} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{10} & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-90} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{-90} \color{blue}{+90} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+90} \\\Leftrightarrow & -1650x+385x& = & 66+90 \\\Leftrightarrow & \color{red}{-1265} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-1265} & & \\\Leftrightarrow & x = \frac{-156}{1265} & & \\ & V = \left\{ \frac{-156}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+30} & = & \color{red}{63x} +28 \\\Leftrightarrow & -420x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & -420x-63x& = & 28-30 \\\Leftrightarrow & \color{red}{-483} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-483} & & \\\Leftrightarrow & x = \frac{2}{483} & & \\ & V = \left\{ \frac{2}{483} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{-110x} +77 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{-60} \\\Leftrightarrow & -264x+110x& = & 77-60 \\\Leftrightarrow & \color{red}{-154} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-154} & & \\\Leftrightarrow & x = \frac{-17}{154} & & \\ & V = \left\{ \frac{-17}{154} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{21x} +2 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -60x-21x& = & 2-8 \\\Leftrightarrow & \color{red}{-81} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-81} & & \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-15} & = & \color{red}{-77x} +6 \\\Leftrightarrow & 165x \color{red}{-15} \color{blue}{+15} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+15} \\\Leftrightarrow & 165x+77x& = & 6+15 \\\Leftrightarrow & \color{red}{242} x& = & 21 \\\Leftrightarrow & x = \frac{21}{242} & & \\ & V = \left\{ \frac{21}{242} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{-72} & = & \color{red}{220x} +99 \\\Leftrightarrow & -528x \color{red}{-72} \color{blue}{+72} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{+72} \\\Leftrightarrow & -528x-220x& = & 99+72 \\\Leftrightarrow & \color{red}{-748} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-748} & & \\\Leftrightarrow & x = \frac{-171}{748} & & \\ & V = \left\{ \frac{-171}{748} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 6x+\frac{9}{5} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 6x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-70} & = & \color{red}{90x} +27 \\\Leftrightarrow & -525x \color{red}{-70} \color{blue}{+70} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{+70} \\\Leftrightarrow & -525x-90x& = & 27+70 \\\Leftrightarrow & \color{red}{-615} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-615} & & \\\Leftrightarrow & x = \frac{-97}{615} & & \\ & V = \left\{ \frac{-97}{615} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{10}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+20} & = & \color{red}{18x} +9 \\\Leftrightarrow & 120x \color{red}{+20} \color{blue}{-20} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{-20} \\\Leftrightarrow & 120x-18x& = & 9-20 \\\Leftrightarrow & \color{red}{102} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{102} & & \\ & V = \left\{ \frac{-11}{102} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{1}{3})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 21x+\frac{7}{3}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+21} & = & \color{red}{-45x} +8 \\\Leftrightarrow & 189x \color{red}{+21} \color{blue}{-21} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{-21} \\\Leftrightarrow & 189x+45x& = & 8-21 \\\Leftrightarrow & \color{red}{234} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{234} & & \\\Leftrightarrow & x = \frac{-1}{18} & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{20}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-40} & = & \color{red}{42x} +63 \\\Leftrightarrow & 140x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & 140x-42x& = & 63+40 \\\Leftrightarrow & \color{red}{98} x& = & 103 \\\Leftrightarrow & x = \frac{103}{98} & & \\ & V = \left\{ \frac{103}{98} \right\} & \\\end{align}\)
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