Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{6})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{168x} +12 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{-168x} & = & \color{red}{168x} +12 \color{blue}{-168x} \color{blue}{+175} \\\Leftrightarrow & 630x-168x& = & 12+175 \\\Leftrightarrow & \color{red}{462} x& = & 187 \\\Leftrightarrow & x = \frac{187}{462} & & \\\Leftrightarrow & x = \frac{17}{42} & & \\ & V = \left\{ \frac{17}{42} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{12})& = & 9x+\frac{7}{10} \\\Leftrightarrow & 25x+\frac{25}{12}& = & 9x+\frac{7}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1500}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{540}{ \color{blue}{60} }x+ \frac{42}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1500x \color{red}{+125} & = & \color{red}{540x} +42 \\\Leftrightarrow & 1500x \color{red}{+125} \color{blue}{-125} \color{blue}{-540x} & = & \color{red}{540x} +42 \color{blue}{-540x} \color{blue}{-125} \\\Leftrightarrow & 1500x-540x& = & 42-125 \\\Leftrightarrow & \color{red}{960} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{960} & & \\ & V = \left\{ \frac{-83}{960} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{18}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+54} \\\Leftrightarrow & 270x+75x& = & 50+54 \\\Leftrightarrow & \color{red}{345} x& = & 104 \\\Leftrightarrow & x = \frac{104}{345} & & \\ & V = \left\{ \frac{104}{345} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+10} & = & \color{red}{15x} +5 \\\Leftrightarrow & 24x \color{red}{+10} \color{blue}{-10} \color{blue}{-15x} & = & \color{red}{15x} +5 \color{blue}{-15x} \color{blue}{-10} \\\Leftrightarrow & 24x-15x& = & 5-10 \\\Leftrightarrow & \color{red}{9} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{9} & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{11})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -14x+\frac{28}{11}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1540}{ \color{blue}{110} }x+ \frac{280}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1540x \color{red}{+280} & = & \color{red}{-330x} +77 \\\Leftrightarrow & -1540x \color{red}{+280} \color{blue}{-280} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{-280} \\\Leftrightarrow & -1540x+330x& = & 77-280 \\\Leftrightarrow & \color{red}{-1210} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{-1210} & & \\\Leftrightarrow & x = \frac{203}{1210} & & \\ & V = \left\{ \frac{203}{1210} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{6}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{+18} \\\Leftrightarrow & -60x+135x& = & 50+18 \\\Leftrightarrow & \color{red}{75} x& = & 68 \\\Leftrightarrow & x = \frac{68}{75} & & \\ & V = \left\{ \frac{68}{75} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{70x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 120x-70x& = & 45+24 \\\Leftrightarrow & \color{red}{50} x& = & 69 \\\Leftrightarrow & x = \frac{69}{50} & & \\ & V = \left\{ \frac{69}{50} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{-140x} +40 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +40 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & 168x+140x& = & 40+105 \\\Leftrightarrow & \color{red}{308} x& = & 145 \\\Leftrightarrow & x = \frac{145}{308} & & \\ & V = \left\{ \frac{145}{308} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{12})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{25}{12}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-900}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{480}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -900x \color{red}{+125} & = & \color{red}{480x} +72 \\\Leftrightarrow & -900x \color{red}{+125} \color{blue}{-125} \color{blue}{-480x} & = & \color{red}{480x} +72 \color{blue}{-480x} \color{blue}{-125} \\\Leftrightarrow & -900x-480x& = & 72-125 \\\Leftrightarrow & \color{red}{-1380} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-1380} & & \\\Leftrightarrow & x = \frac{53}{1380} & & \\ & V = \left\{ \frac{53}{1380} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{25}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{125}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-125} & = & \color{red}{245x} +28 \\\Leftrightarrow & 700x \color{red}{-125} \color{blue}{+125} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+125} \\\Leftrightarrow & 700x-245x& = & 28+125 \\\Leftrightarrow & \color{red}{455} x& = & 153 \\\Leftrightarrow & x = \frac{153}{455} & & \\ & V = \left\{ \frac{153}{455} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-9} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-9} \color{blue}{+9} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+9} \\\Leftrightarrow & 60x+25x& = & 6+9 \\\Leftrightarrow & \color{red}{85} x& = & 15 \\\Leftrightarrow & x = \frac{15}{85} & & \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-9} \\\Leftrightarrow & -60x+70x& = & 3-9 \\\Leftrightarrow & \color{red}{10} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{10} & & \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)