Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{11})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{16}{11}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+144} & = & \color{red}{891x} +44 \\\Leftrightarrow & -792x \color{red}{+144} \color{blue}{-144} \color{blue}{-891x} & = & \color{red}{891x} +44 \color{blue}{-891x} \color{blue}{-144} \\\Leftrightarrow & -792x-891x& = & 44-144 \\\Leftrightarrow & \color{red}{-1683} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-1683} & & \\\Leftrightarrow & x = \frac{100}{1683} & & \\ & V = \left\{ \frac{100}{1683} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 70-66 \\\Leftrightarrow & \color{red}{77} x& = & 4 \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{-72} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 360x \color{red}{-72} \color{blue}{+72} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+72} \\\Leftrightarrow & 360x+75x& = & 10+72 \\\Leftrightarrow & \color{red}{435} x& = & 82 \\\Leftrightarrow & x = \frac{82}{435} & & \\ & V = \left\{ \frac{82}{435} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-100} & = & \color{red}{-105x} +21 \\\Leftrightarrow & -240x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +21 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & -240x+105x& = & 21+100 \\\Leftrightarrow & \color{red}{-135} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-135} & & \\\Leftrightarrow & x = \frac{-121}{135} & & \\ & V = \left\{ \frac{-121}{135} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-60} & = & \color{red}{189x} +28 \\\Leftrightarrow & -168x \color{red}{-60} \color{blue}{+60} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+60} \\\Leftrightarrow & -168x-189x& = & 28+60 \\\Leftrightarrow & \color{red}{-357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-357} & & \\\Leftrightarrow & x = \frac{-88}{357} & & \\ & V = \left\{ \frac{-88}{357} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{6})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{-54x} +20 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{+54x} & = & \color{red}{-54x} +20 \color{blue}{+54x} \color{blue}{-105} \\\Leftrightarrow & 252x+54x& = & 20-105 \\\Leftrightarrow & \color{red}{306} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{306} & & \\\Leftrightarrow & x = \frac{-5}{18} & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+8} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -54x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -54x+63x& = & 4-8 \\\Leftrightarrow & \color{red}{9} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -60x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & -60x+70x& = & 15-24 \\\Leftrightarrow & \color{red}{10} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{10} & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{175x} +49 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{+100} \\\Leftrightarrow & 560x-175x& = & 49+100 \\\Leftrightarrow & \color{red}{385} x& = & 149 \\\Leftrightarrow & x = \frac{149}{385} & & \\ & V = \left\{ \frac{149}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{50x} +25 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 120x-50x& = & 25-12 \\\Leftrightarrow & \color{red}{70} x& = & 13 \\\Leftrightarrow & x = \frac{13}{70} & & \\ & V = \left\{ \frac{13}{70} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-224}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -224x \color{red}{+40} & = & \color{red}{98x} +49 \\\Leftrightarrow & -224x \color{red}{+40} \color{blue}{-40} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{-40} \\\Leftrightarrow & -224x-98x& = & 49-40 \\\Leftrightarrow & \color{red}{-322} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-322} & & \\\Leftrightarrow & x = \frac{-9}{322} & & \\ & V = \left\{ \frac{-9}{322} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{75x} +6 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{-40} \\\Leftrightarrow & 120x-75x& = & 6-40 \\\Leftrightarrow & \color{red}{45} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{45} & & \\ & V = \left\{ \frac{-34}{45} \right\} & \\\end{align}\)