Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-24} & = & \color{red}{90x} +15 \\\Leftrightarrow & 80x \color{red}{-24} \color{blue}{+24} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+24} \\\Leftrightarrow & 80x-90x& = & 15+24 \\\Leftrightarrow & \color{red}{-10} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-10} & & \\\Leftrightarrow & x = \frac{-39}{10} & & \\ & V = \left\{ \frac{-39}{10} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 9x+\frac{15}{8}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{504}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 504x \color{red}{+105} & = & \color{red}{-112x} +48 \\\Leftrightarrow & 504x \color{red}{+105} \color{blue}{-105} \color{blue}{+112x} & = & \color{red}{-112x} +48 \color{blue}{+112x} \color{blue}{-105} \\\Leftrightarrow & 504x+112x& = & 48-105 \\\Leftrightarrow & \color{red}{616} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{616} & & \\ & V = \left\{ \frac{-57}{616} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -25x+\frac{25}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-550}{ \color{blue}{22} }x+ \frac{50}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -550x \color{red}{+50} & = & \color{red}{154x} +99 \\\Leftrightarrow & -550x \color{red}{+50} \color{blue}{-50} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-50} \\\Leftrightarrow & -550x-154x& = & 99-50 \\\Leftrightarrow & \color{red}{-704} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-704} & & \\\Leftrightarrow & x = \frac{-49}{704} & & \\ & V = \left\{ \frac{-49}{704} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{-120x} +28 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{+120x} & = & \color{red}{-120x} +28 \color{blue}{+120x} \color{blue}{+105} \\\Leftrightarrow & -560x+120x& = & 28+105 \\\Leftrightarrow & \color{red}{-440} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-440} & & \\\Leftrightarrow & x = \frac{-133}{440} & & \\ & V = \left\{ \frac{-133}{440} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+40} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -96x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & -96x+42x& = & 5-40 \\\Leftrightarrow & \color{red}{-54} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-54} & & \\\Leftrightarrow & x = \frac{35}{54} & & \\ & V = \left\{ \frac{35}{54} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{3})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{-54x} +5 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & -48x+54x& = & 5-16 \\\Leftrightarrow & \color{red}{6} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{6} & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{9}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{70x} +35 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & -60x-70x& = & 35+18 \\\Leftrightarrow & \color{red}{-130} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-130} & & \\\Leftrightarrow & x = \frac{-53}{130} & & \\ & V = \left\{ \frac{-53}{130} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{45x} +12 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{+40} \\\Leftrightarrow & -120x-45x& = & 12+40 \\\Leftrightarrow & \color{red}{-165} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-165} & & \\\Leftrightarrow & x = \frac{-52}{165} & & \\ & V = \left\{ \frac{-52}{165} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{18}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+126} & = & \color{red}{175x} +50 \\\Leftrightarrow & 840x \color{red}{+126} \color{blue}{-126} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-126} \\\Leftrightarrow & 840x-175x& = & 50-126 \\\Leftrightarrow & \color{red}{665} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{665} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{11})& = & -9x+\frac{3}{11} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+8} & = & \color{red}{-99x} +3 \\\Leftrightarrow & -88x \color{red}{+8} \color{blue}{-8} \color{blue}{+99x} & = & \color{red}{-99x} +3 \color{blue}{+99x} \color{blue}{-8} \\\Leftrightarrow & -88x+99x& = & 3-8 \\\Leftrightarrow & \color{red}{11} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-20} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 270x \color{red}{-20} \color{blue}{+20} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{+20} \\\Leftrightarrow & 270x+225x& = & 54+20 \\\Leftrightarrow & \color{red}{495} x& = & 74 \\\Leftrightarrow & x = \frac{74}{495} & & \\ & V = \left\{ \frac{74}{495} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{-84x} +28 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{+30} \\\Leftrightarrow & -315x+84x& = & 28+30 \\\Leftrightarrow & \color{red}{-231} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-231} & & \\\Leftrightarrow & x = \frac{-58}{231} & & \\ & V = \left\{ \frac{-58}{231} \right\} & \\\end{align}\)