Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{5}{9} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{-108} & = & \color{red}{225x} +25 \\\Leftrightarrow & -1080x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +25 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & -1080x-225x& = & 25+108 \\\Leftrightarrow & \color{red}{-1305} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-1305} & & \\\Leftrightarrow & x = \frac{-133}{1305} & & \\ & V = \left\{ \frac{-133}{1305} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+40} & = & \color{red}{-405x} +54 \\\Leftrightarrow & 900x \color{red}{+40} \color{blue}{-40} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{-40} \\\Leftrightarrow & 900x+405x& = & 54-40 \\\Leftrightarrow & \color{red}{1305} x& = & 14 \\\Leftrightarrow & x = \frac{14}{1305} & & \\ & V = \left\{ \frac{14}{1305} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-140} & = & \color{red}{-315x} +18 \\\Leftrightarrow & -1260x \color{red}{-140} \color{blue}{+140} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+140} \\\Leftrightarrow & -1260x+315x& = & 18+140 \\\Leftrightarrow & \color{red}{-945} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-945} & & \\\Leftrightarrow & x = \frac{-158}{945} & & \\ & V = \left\{ \frac{-158}{945} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{245x} +63 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & 350x-245x& = & 63+50 \\\Leftrightarrow & \color{red}{105} x& = & 113 \\\Leftrightarrow & x = \frac{113}{105} & & \\ & V = \left\{ \frac{113}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{6})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 28x+\frac{35}{6}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{-90x} +21 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{-175} \\\Leftrightarrow & 840x+90x& = & 21-175 \\\Leftrightarrow & \color{red}{930} x& = & -154 \\\Leftrightarrow & x = \frac{-154}{930} & & \\\Leftrightarrow & x = \frac{-77}{465} & & \\ & V = \left\{ \frac{-77}{465} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{-100} & = & \color{red}{-280x} +42 \\\Leftrightarrow & 875x \color{red}{-100} \color{blue}{+100} \color{blue}{+280x} & = & \color{red}{-280x} +42 \color{blue}{+280x} \color{blue}{+100} \\\Leftrightarrow & 875x+280x& = & 42+100 \\\Leftrightarrow & \color{red}{1155} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1155} & & \\ & V = \left\{ \frac{142}{1155} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{7})& = & -2x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{20}{7}& = & -2x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{200}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+200} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 1050x \color{red}{+200} \color{blue}{-200} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-200} \\\Leftrightarrow & 1050x+140x& = & 63-200 \\\Leftrightarrow & \color{red}{1190} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{1190} & & \\ & V = \left\{ \frac{-137}{1190} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 4x+\frac{7}{9} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 4x+\frac{7}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-900}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{28}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -900x \color{red}{-135} & = & \color{red}{144x} +28 \\\Leftrightarrow & -900x \color{red}{-135} \color{blue}{+135} \color{blue}{-144x} & = & \color{red}{144x} +28 \color{blue}{-144x} \color{blue}{+135} \\\Leftrightarrow & -900x-144x& = & 28+135 \\\Leftrightarrow & \color{red}{-1044} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-1044} & & \\\Leftrightarrow & x = \frac{-163}{1044} & & \\ & V = \left\{ \frac{-163}{1044} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{+140} & = & \color{red}{-150x} +21 \\\Leftrightarrow & 840x \color{red}{+140} \color{blue}{-140} \color{blue}{+150x} & = & \color{red}{-150x} +21 \color{blue}{+150x} \color{blue}{-140} \\\Leftrightarrow & 840x+150x& = & 21-140 \\\Leftrightarrow & \color{red}{990} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{990} & & \\ & V = \left\{ \frac{-119}{990} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{+180} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -3300x \color{red}{+180} \color{blue}{-180} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{-180} \\\Leftrightarrow & -3300x+770x& = & 99-180 \\\Leftrightarrow & \color{red}{-2530} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-2530} & & \\\Leftrightarrow & x = \frac{81}{2530} & & \\ & V = \left\{ \frac{81}{2530} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+40} & = & \color{red}{54x} +5 \\\Leftrightarrow & 48x \color{red}{+40} \color{blue}{-40} \color{blue}{-54x} & = & \color{red}{54x} +5 \color{blue}{-54x} \color{blue}{-40} \\\Leftrightarrow & 48x-54x& = & 5-40 \\\Leftrightarrow & \color{red}{-6} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-6} & & \\\Leftrightarrow & x = \frac{35}{6} & & \\ & V = \left\{ \frac{35}{6} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{8}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-32} & = & \color{red}{132x} +33 \\\Leftrightarrow & 352x \color{red}{-32} \color{blue}{+32} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{+32} \\\Leftrightarrow & 352x-132x& = & 33+32 \\\Leftrightarrow & \color{red}{220} x& = & 65 \\\Leftrightarrow & x = \frac{65}{220} & & \\\Leftrightarrow & x = \frac{13}{44} & & \\ & V = \left\{ \frac{13}{44} \right\} & \\\end{align}\)