Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 270x-75x& = & 20+72 \\\Leftrightarrow & \color{red}{195} x& = & 92 \\\Leftrightarrow & x = \frac{92}{195} & & \\ & V = \left\{ \frac{92}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -35x+4& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x+ \frac{20}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{+20} & = & \color{red}{45x} +4 \\\Leftrightarrow & -175x \color{red}{+20} \color{blue}{-20} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{-20} \\\Leftrightarrow & -175x-45x& = & 4-20 \\\Leftrightarrow & \color{red}{-220} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-220} & & \\\Leftrightarrow & x = \frac{4}{55} & & \\ & V = \left\{ \frac{4}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-880}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -880x \color{red}{+120} & = & \color{red}{-990x} +99 \\\Leftrightarrow & -880x \color{red}{+120} \color{blue}{-120} \color{blue}{+990x} & = & \color{red}{-990x} +99 \color{blue}{+990x} \color{blue}{-120} \\\Leftrightarrow & -880x+990x& = & 99-120 \\\Leftrightarrow & \color{red}{110} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{110} & & \\ & V = \left\{ \frac{-21}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -8x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-168x} +28 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+168x} & = & \color{red}{-168x} +28 \color{blue}{+168x} \color{blue}{-30} \\\Leftrightarrow & 525x+168x& = & 28-30 \\\Leftrightarrow & \color{red}{693} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{693} & & \\ & V = \left\{ \frac{-2}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+8} & = & \color{red}{63x} +12 \\\Leftrightarrow & 90x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & 90x-63x& = & 12-8 \\\Leftrightarrow & \color{red}{27} x& = & 4 \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-126}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{-63x} +3 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{+63x} & = & \color{red}{-63x} +3 \color{blue}{+63x} \color{blue}{-30} \\\Leftrightarrow & -126x+63x& = & 3-30 \\\Leftrightarrow & \color{red}{-63} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-63} & & \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{11})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 4x-\frac{4}{11}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{36}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-36} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 396x \color{red}{-36} \color{blue}{+36} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+36} \\\Leftrightarrow & 396x+297x& = & 44+36 \\\Leftrightarrow & \color{red}{693} x& = & 80 \\\Leftrightarrow & x = \frac{80}{693} & & \\ & V = \left\{ \frac{80}{693} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{15}{8}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{-392x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{+392x} & = & \color{red}{-392x} +48 \color{blue}{+392x} \color{blue}{-105} \\\Leftrightarrow & -560x+392x& = & 48-105 \\\Leftrightarrow & \color{red}{-168} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-168} & & \\\Leftrightarrow & x = \frac{19}{56} & & \\ & V = \left\{ \frac{19}{56} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+40} & = & \color{red}{42x} +15 \\\Leftrightarrow & -96x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +15 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & -96x-42x& = & 15-40 \\\Leftrightarrow & \color{red}{-138} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-138} & & \\\Leftrightarrow & x = \frac{25}{138} & & \\ & V = \left\{ \frac{25}{138} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+50} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 140x \color{red}{+50} \color{blue}{-50} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-50} \\\Leftrightarrow & 140x+175x& = & 28-50 \\\Leftrightarrow & \color{red}{315} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{315} & & \\ & V = \left\{ \frac{-22}{315} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{5})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -12x-\frac{24}{5}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{144}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-144} & = & \color{red}{150x} +35 \\\Leftrightarrow & -360x \color{red}{-144} \color{blue}{+144} \color{blue}{-150x} & = & \color{red}{150x} +35 \color{blue}{-150x} \color{blue}{+144} \\\Leftrightarrow & -360x-150x& = & 35+144 \\\Leftrightarrow & \color{red}{-510} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-510} & & \\\Leftrightarrow & x = \frac{-179}{510} & & \\ & V = \left\{ \frac{-179}{510} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{+40} & = & \color{red}{252x} +63 \\\Leftrightarrow & -700x \color{red}{+40} \color{blue}{-40} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-40} \\\Leftrightarrow & -700x-252x& = & 63-40 \\\Leftrightarrow & \color{red}{-952} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-952} & & \\\Leftrightarrow & x = \frac{-23}{952} & & \\ & V = \left\{ \frac{-23}{952} \right\} & \\\end{align}\)