Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{10})& = & -4x+\frac{9}{10} \\\Leftrightarrow & 9x+\frac{9}{10}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+9} & = & \color{red}{-40x} +9 \\\Leftrightarrow & 90x \color{red}{+9} \color{blue}{-9} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{-9} \\\Leftrightarrow & 90x+40x& = & 9-9 \\\Leftrightarrow & \color{red}{130} x& = & 0 \\\Leftrightarrow & x = \frac{0}{130} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +70 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 70-18 \\\Leftrightarrow & \color{red}{-273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-273} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{-385x} +20 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 1650x+385x& = & 20-132 \\\Leftrightarrow & \color{red}{2035} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{2035} & & \\ & V = \left\{ \frac{-112}{2035} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{10}{3}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{40}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-40} & = & \color{red}{108x} +9 \\\Leftrightarrow & -240x \color{red}{-40} \color{blue}{+40} \color{blue}{-108x} & = & \color{red}{108x} +9 \color{blue}{-108x} \color{blue}{+40} \\\Leftrightarrow & -240x-108x& = & 9+40 \\\Leftrightarrow & \color{red}{-348} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-348} & & \\\Leftrightarrow & x = \frac{-49}{348} & & \\ & V = \left\{ \frac{-49}{348} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{7})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{25}{7}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{50}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+50} & = & \color{red}{112x} +49 \\\Leftrightarrow & -210x \color{red}{+50} \color{blue}{-50} \color{blue}{-112x} & = & \color{red}{112x} +49 \color{blue}{-112x} \color{blue}{-50} \\\Leftrightarrow & -210x-112x& = & 49-50 \\\Leftrightarrow & \color{red}{-322} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-322} & & \\\Leftrightarrow & x = \frac{1}{322} & & \\ & V = \left\{ \frac{1}{322} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 300x+105x& = & 50-36 \\\Leftrightarrow & \color{red}{405} x& = & 14 \\\Leftrightarrow & x = \frac{14}{405} & & \\ & V = \left\{ \frac{14}{405} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+54} & = & \color{red}{75x} +10 \\\Leftrightarrow & 270x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & 270x-75x& = & 10-54 \\\Leftrightarrow & \color{red}{195} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{195} & & \\ & V = \left\{ \frac{-44}{195} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & 150x+35x& = & 6-12 \\\Leftrightarrow & \color{red}{185} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{185} & & \\ & V = \left\{ \frac{-6}{185} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-30} & = & \color{red}{-245x} +28 \\\Leftrightarrow & 525x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & 525x+245x& = & 28+30 \\\Leftrightarrow & \color{red}{770} x& = & 58 \\\Leftrightarrow & x = \frac{58}{770} & & \\\Leftrightarrow & x = \frac{29}{385} & & \\ & V = \left\{ \frac{29}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{8}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{216}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 216x \color{red}{+16} & = & \color{red}{-126x} +81 \\\Leftrightarrow & 216x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & 216x+126x& = & 81-16 \\\Leftrightarrow & \color{red}{342} x& = & 65 \\\Leftrightarrow & x = \frac{65}{342} & & \\ & V = \left\{ \frac{65}{342} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{3})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{9x} +10 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{-9x} & = & \color{red}{9x} +10 \color{blue}{-9x} \color{blue}{-8} \\\Leftrightarrow & 30x-9x& = & 10-8 \\\Leftrightarrow & \color{red}{21} x& = & 2 \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{5})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 14x+\frac{14}{5}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x+ \frac{112}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{+112} & = & \color{red}{360x} +25 \\\Leftrightarrow & 560x \color{red}{+112} \color{blue}{-112} \color{blue}{-360x} & = & \color{red}{360x} +25 \color{blue}{-360x} \color{blue}{-112} \\\Leftrightarrow & 560x-360x& = & 25-112 \\\Leftrightarrow & \color{red}{200} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{200} & & \\ & V = \left\{ \frac{-87}{200} \right\} & \\\end{align}\)