Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{16}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+16} & = & \color{red}{49x} +3 \\\Leftrightarrow & 140x \color{red}{+16} \color{blue}{-16} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-16} \\\Leftrightarrow & 140x-49x& = & 3-16 \\\Leftrightarrow & \color{red}{91} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{91} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-54} & = & \color{red}{-315x} +28 \\\Leftrightarrow & 378x \color{red}{-54} \color{blue}{+54} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{+54} \\\Leftrightarrow & 378x+315x& = & 28+54 \\\Leftrightarrow & \color{red}{693} x& = & 82 \\\Leftrightarrow & x = \frac{82}{693} & & \\ & V = \left\{ \frac{82}{693} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{6})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{25}{6}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{18x} +4 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{-18x} & = & \color{red}{18x} +4 \color{blue}{-18x} \color{blue}{-25} \\\Leftrightarrow & -120x-18x& = & 4-25 \\\Leftrightarrow & \color{red}{-138} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-138} & & \\\Leftrightarrow & x = \frac{7}{46} & & \\ & V = \left\{ \frac{7}{46} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{4})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{9}{4}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{27}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-27} & = & \color{red}{60x} +40 \\\Leftrightarrow & 144x \color{red}{-27} \color{blue}{+27} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{+27} \\\Leftrightarrow & 144x-60x& = & 40+27 \\\Leftrightarrow & \color{red}{84} x& = & 67 \\\Leftrightarrow & x = \frac{67}{84} & & \\ & V = \left\{ \frac{67}{84} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-63} & = & \color{red}{175x} +50 \\\Leftrightarrow & 210x \color{red}{-63} \color{blue}{+63} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+63} \\\Leftrightarrow & 210x-175x& = & 50+63 \\\Leftrightarrow & \color{red}{35} x& = & 113 \\\Leftrightarrow & x = \frac{113}{35} & & \\ & V = \left\{ \frac{113}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{11})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+144} & = & \color{red}{297x} +44 \\\Leftrightarrow & -1980x \color{red}{+144} \color{blue}{-144} \color{blue}{-297x} & = & \color{red}{297x} +44 \color{blue}{-297x} \color{blue}{-144} \\\Leftrightarrow & -1980x-297x& = & 44-144 \\\Leftrightarrow & \color{red}{-2277} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-2277} & & \\\Leftrightarrow & x = \frac{100}{2277} & & \\ & V = \left\{ \frac{100}{2277} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{3})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 4x+\frac{4}{3}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+28} & = & \color{red}{-63x} +12 \\\Leftrightarrow & 84x \color{red}{+28} \color{blue}{-28} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{-28} \\\Leftrightarrow & 84x+63x& = & 12-28 \\\Leftrightarrow & \color{red}{147} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{147} & & \\ & V = \left\{ \frac{-16}{147} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{15}{4}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{+135} & = & \color{red}{-252x} +32 \\\Leftrightarrow & 432x \color{red}{+135} \color{blue}{-135} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{-135} \\\Leftrightarrow & 432x+252x& = & 32-135 \\\Leftrightarrow & \color{red}{684} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{684} & & \\ & V = \left\{ \frac{-103}{684} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{16}{3}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x- \frac{160}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{-160} & = & \color{red}{-270x} +27 \\\Leftrightarrow & -600x \color{red}{-160} \color{blue}{+160} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{+160} \\\Leftrightarrow & -600x+270x& = & 27+160 \\\Leftrightarrow & \color{red}{-330} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-330} & & \\\Leftrightarrow & x = \frac{-17}{30} & & \\ & V = \left\{ \frac{-17}{30} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -16x-\frac{12}{11}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1056}{ \color{blue}{66} }x- \frac{72}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1056x \color{red}{-72} & = & \color{red}{462x} +77 \\\Leftrightarrow & -1056x \color{red}{-72} \color{blue}{+72} \color{blue}{-462x} & = & \color{red}{462x} +77 \color{blue}{-462x} \color{blue}{+72} \\\Leftrightarrow & -1056x-462x& = & 77+72 \\\Leftrightarrow & \color{red}{-1518} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1518} & & \\\Leftrightarrow & x = \frac{-149}{1518} & & \\ & V = \left\{ \frac{-149}{1518} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -16x+\frac{20}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{180}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+180} & = & \color{red}{693x} +88 \\\Leftrightarrow & -1584x \color{red}{+180} \color{blue}{-180} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{-180} \\\Leftrightarrow & -1584x-693x& = & 88-180 \\\Leftrightarrow & \color{red}{-2277} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-2277} & & \\\Leftrightarrow & x = \frac{4}{99} & & \\ & V = \left\{ \frac{4}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -35x-\frac{35}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-175} & = & \color{red}{135x} +6 \\\Leftrightarrow & -525x \color{red}{-175} \color{blue}{+175} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{+175} \\\Leftrightarrow & -525x-135x& = & 6+175 \\\Leftrightarrow & \color{red}{-660} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-660} & & \\\Leftrightarrow & x = \frac{-181}{660} & & \\ & V = \left\{ \frac{-181}{660} \right\} & \\\end{align}\)