Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{3})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{-165x} +30 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +30 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 264x+165x& = & 30+88 \\\Leftrightarrow & \color{red}{429} x& = & 118 \\\Leftrightarrow & x = \frac{118}{429} & & \\ & V = \left\{ \frac{118}{429} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{-108} & = & \color{red}{-405x} +50 \\\Leftrightarrow & -810x \color{red}{-108} \color{blue}{+108} \color{blue}{+405x} & = & \color{red}{-405x} +50 \color{blue}{+405x} \color{blue}{+108} \\\Leftrightarrow & -810x+405x& = & 50+108 \\\Leftrightarrow & \color{red}{-405} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-405} & & \\\Leftrightarrow & x = \frac{-158}{405} & & \\ & V = \left\{ \frac{-158}{405} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-10} & = & \color{red}{-44x} +6 \\\Leftrightarrow & 165x \color{red}{-10} \color{blue}{+10} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{+10} \\\Leftrightarrow & 165x+44x& = & 6+10 \\\Leftrightarrow & \color{red}{209} x& = & 16 \\\Leftrightarrow & x = \frac{16}{209} & & \\ & V = \left\{ \frac{16}{209} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-60} & = & \color{red}{-147x} +28 \\\Leftrightarrow & 210x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & 210x+147x& = & 28+60 \\\Leftrightarrow & \color{red}{357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{357} & & \\ & V = \left\{ \frac{88}{357} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-27} & = & \color{red}{60x} +50 \\\Leftrightarrow & -225x \color{red}{-27} \color{blue}{+27} \color{blue}{-60x} & = & \color{red}{60x} +50 \color{blue}{-60x} \color{blue}{+27} \\\Leftrightarrow & -225x-60x& = & 50+27 \\\Leftrightarrow & \color{red}{-285} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-285} & & \\\Leftrightarrow & x = \frac{-77}{285} & & \\ & V = \left\{ \frac{-77}{285} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{8}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{105x} +6 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{+40} \\\Leftrightarrow & 180x-105x& = & 6+40 \\\Leftrightarrow & \color{red}{75} x& = & 46 \\\Leftrightarrow & x = \frac{46}{75} & & \\ & V = \left\{ \frac{46}{75} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{70x} +9 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -100x-70x& = & 9+12 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{2})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{21}{2}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+63} & = & \color{red}{18x} +8 \\\Leftrightarrow & 84x \color{red}{+63} \color{blue}{-63} \color{blue}{-18x} & = & \color{red}{18x} +8 \color{blue}{-18x} \color{blue}{-63} \\\Leftrightarrow & 84x-18x& = & 8-63 \\\Leftrightarrow & \color{red}{66} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{66} & & \\\Leftrightarrow & x = \frac{-5}{6} & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & -3x+\frac{9}{5} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+50} & = & \color{red}{-105x} +63 \\\Leftrightarrow & -875x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +63 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -875x+105x& = & 63-50 \\\Leftrightarrow & \color{red}{-770} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-770} & & \\\Leftrightarrow & x = \frac{-13}{770} & & \\ & V = \left\{ \frac{-13}{770} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{231x} +21 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 495x-231x& = & 21-220 \\\Leftrightarrow & \color{red}{264} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{264} & & \\ & V = \left\{ \frac{-199}{264} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -25x+\frac{25}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x+ \frac{225}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{+225} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -2475x \color{red}{+225} \color{blue}{-225} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{-225} \\\Leftrightarrow & -2475x+693x& = & 88-225 \\\Leftrightarrow & \color{red}{-1782} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-1782} & & \\\Leftrightarrow & x = \frac{137}{1782} & & \\ & V = \left\{ \frac{137}{1782} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -540x+225x& = & 10-108 \\\Leftrightarrow & \color{red}{-315} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-315} & & \\\Leftrightarrow & x = \frac{14}{45} & & \\ & V = \left\{ \frac{14}{45} \right\} & \\\end{align}\)