Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 60x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{6})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-840}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -840x \color{red}{+175} & = & \color{red}{-270x} +48 \\\Leftrightarrow & -840x \color{red}{+175} \color{blue}{-175} \color{blue}{+270x} & = & \color{red}{-270x} +48 \color{blue}{+270x} \color{blue}{-175} \\\Leftrightarrow & -840x+270x& = & 48-175 \\\Leftrightarrow & \color{red}{-570} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-570} & & \\\Leftrightarrow & x = \frac{127}{570} & & \\ & V = \left\{ \frac{127}{570} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & 525x+245x& = & 42-30 \\\Leftrightarrow & \color{red}{770} x& = & 12 \\\Leftrightarrow & x = \frac{12}{770} & & \\\Leftrightarrow & x = \frac{6}{385} & & \\ & V = \left\{ \frac{6}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{3})& = & -3x+\frac{7}{3} \\\Leftrightarrow & -14x+\frac{35}{3}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+35} & = & \color{red}{-9x} +7 \\\Leftrightarrow & -42x \color{red}{+35} \color{blue}{-35} \color{blue}{+9x} & = & \color{red}{-9x} +7 \color{blue}{+9x} \color{blue}{-35} \\\Leftrightarrow & -42x+9x& = & 7-35 \\\Leftrightarrow & \color{red}{-33} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-33} & & \\\Leftrightarrow & x = \frac{28}{33} & & \\ & V = \left\{ \frac{28}{33} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{2})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-275} & = & \color{red}{44x} +12 \\\Leftrightarrow & 550x \color{red}{-275} \color{blue}{+275} \color{blue}{-44x} & = & \color{red}{44x} +12 \color{blue}{-44x} \color{blue}{+275} \\\Leftrightarrow & 550x-44x& = & 12+275 \\\Leftrightarrow & \color{red}{506} x& = & 287 \\\Leftrightarrow & x = \frac{287}{506} & & \\ & V = \left\{ \frac{287}{506} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{3})& = & -6x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{25}{3}& = & -6x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+275} & = & \color{red}{-198x} +6 \\\Leftrightarrow & 825x \color{red}{+275} \color{blue}{-275} \color{blue}{+198x} & = & \color{red}{-198x} +6 \color{blue}{+198x} \color{blue}{-275} \\\Leftrightarrow & 825x+198x& = & 6-275 \\\Leftrightarrow & \color{red}{1023} x& = & -269 \\\Leftrightarrow & x = \frac{-269}{1023} & & \\ & V = \left\{ \frac{-269}{1023} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{3})& = & 6x+\frac{3}{10} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{350}{ \color{blue}{30} })& = & (\frac{180}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-350} & = & \color{red}{180x} +9 \\\Leftrightarrow & 1050x \color{red}{-350} \color{blue}{+350} \color{blue}{-180x} & = & \color{red}{180x} +9 \color{blue}{-180x} \color{blue}{+350} \\\Leftrightarrow & 1050x-180x& = & 9+350 \\\Leftrightarrow & \color{red}{870} x& = & 359 \\\Leftrightarrow & x = \frac{359}{870} & & \\ & V = \left\{ \frac{359}{870} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & -350x+245x& = & 42+30 \\\Leftrightarrow & \color{red}{-105} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-105} & & \\\Leftrightarrow & x = \frac{-24}{35} & & \\ & V = \left\{ \frac{-24}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-18} & = & \color{red}{70x} +15 \\\Leftrightarrow & -90x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & -90x-70x& = & 15+18 \\\Leftrightarrow & \color{red}{-160} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-160} & & \\\Leftrightarrow & x = \frac{-33}{160} & & \\ & V = \left\{ \frac{-33}{160} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 20x+\frac{12}{11}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2640}{ \color{blue}{132} }x+ \frac{144}{ \color{blue}{132} })& = & (\frac{-396}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2640x \color{red}{+144} & = & \color{red}{-396x} +55 \\\Leftrightarrow & 2640x \color{red}{+144} \color{blue}{-144} \color{blue}{+396x} & = & \color{red}{-396x} +55 \color{blue}{+396x} \color{blue}{-144} \\\Leftrightarrow & 2640x+396x& = & 55-144 \\\Leftrightarrow & \color{red}{3036} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{3036} & & \\ & V = \left\{ \frac{-89}{3036} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{7}{10} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-320x} +28 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+320x} & = & \color{red}{-320x} +28 \color{blue}{+320x} \color{blue}{+105} \\\Leftrightarrow & -840x+320x& = & 28+105 \\\Leftrightarrow & \color{red}{-520} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-520} & & \\\Leftrightarrow & x = \frac{-133}{520} & & \\ & V = \left\{ \frac{-133}{520} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{9}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+81} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -270x \color{red}{+81} \color{blue}{-81} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-81} \\\Leftrightarrow & -270x+315x& = & 20-81 \\\Leftrightarrow & \color{red}{45} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{45} & & \\ & V = \left\{ \frac{-61}{45} \right\} & \\\end{align}\)