Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+108} & = & \color{red}{360x} +10 \\\Leftrightarrow & -810x \color{red}{+108} \color{blue}{-108} \color{blue}{-360x} & = & \color{red}{360x} +10 \color{blue}{-360x} \color{blue}{-108} \\\Leftrightarrow & -810x-360x& = & 10-108 \\\Leftrightarrow & \color{red}{-1170} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-1170} & & \\\Leftrightarrow & x = \frac{49}{585} & & \\ & V = \left\{ \frac{49}{585} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-192} & = & \color{red}{200x} +45 \\\Leftrightarrow & 480x \color{red}{-192} \color{blue}{+192} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{+192} \\\Leftrightarrow & 480x-200x& = & 45+192 \\\Leftrightarrow & \color{red}{280} x& = & 237 \\\Leftrightarrow & x = \frac{237}{280} & & \\ & V = \left\{ \frac{237}{280} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+220} & = & \color{red}{99x} +24 \\\Leftrightarrow & -660x \color{red}{+220} \color{blue}{-220} \color{blue}{-99x} & = & \color{red}{99x} +24 \color{blue}{-99x} \color{blue}{-220} \\\Leftrightarrow & -660x-99x& = & 24-220 \\\Leftrightarrow & \color{red}{-759} x& = & -196 \\\Leftrightarrow & x = \frac{-196}{-759} & & \\\Leftrightarrow & x = \frac{196}{759} & & \\ & V = \left\{ \frac{196}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -112x+49x& = & 9+20 \\\Leftrightarrow & \color{red}{-63} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-63} & & \\\Leftrightarrow & x = \frac{-29}{63} & & \\ & V = \left\{ \frac{-29}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -6x-\frac{6}{11}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{539x} +33 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{-539x} & = & \color{red}{539x} +33 \color{blue}{-539x} \color{blue}{+42} \\\Leftrightarrow & -462x-539x& = & 33+42 \\\Leftrightarrow & \color{red}{-1001} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-1001} & & \\\Leftrightarrow & x = \frac{-75}{1001} & & \\ & V = \left\{ \frac{-75}{1001} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{9})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{14}{9}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x+ \frac{98}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{+98} & = & \color{red}{126x} +90 \\\Leftrightarrow & 1323x \color{red}{+98} \color{blue}{-98} \color{blue}{-126x} & = & \color{red}{126x} +90 \color{blue}{-126x} \color{blue}{-98} \\\Leftrightarrow & 1323x-126x& = & 90-98 \\\Leftrightarrow & \color{red}{1197} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{1197} & & \\ & V = \left\{ \frac{-8}{1197} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{2})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+275} & = & \color{red}{154x} +10 \\\Leftrightarrow & -220x \color{red}{+275} \color{blue}{-275} \color{blue}{-154x} & = & \color{red}{154x} +10 \color{blue}{-154x} \color{blue}{-275} \\\Leftrightarrow & -220x-154x& = & 10-275 \\\Leftrightarrow & \color{red}{-374} x& = & -265 \\\Leftrightarrow & x = \frac{-265}{-374} & & \\\Leftrightarrow & x = \frac{265}{374} & & \\ & V = \left\{ \frac{265}{374} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{10})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{9}{10}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{50}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-81} & = & \color{red}{-450x} +50 \\\Leftrightarrow & 540x \color{red}{-81} \color{blue}{+81} \color{blue}{+450x} & = & \color{red}{-450x} +50 \color{blue}{+450x} \color{blue}{+81} \\\Leftrightarrow & 540x+450x& = & 50+81 \\\Leftrightarrow & \color{red}{990} x& = & 131 \\\Leftrightarrow & x = \frac{131}{990} & & \\ & V = \left\{ \frac{131}{990} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -880x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -880x-385x& = & 30-132 \\\Leftrightarrow & \color{red}{-1265} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-1265} & & \\\Leftrightarrow & x = \frac{102}{1265} & & \\ & V = \left\{ \frac{102}{1265} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 120x+70x& = & 45-48 \\\Leftrightarrow & \color{red}{190} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{190} & & \\ & V = \left\{ \frac{-3}{190} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{10}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+10} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 54x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & 54x+63x& = & 30-10 \\\Leftrightarrow & \color{red}{117} x& = & 20 \\\Leftrightarrow & x = \frac{20}{117} & & \\ & V = \left\{ \frac{20}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{7})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -15x-\frac{9}{7}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-99} & = & \color{red}{616x} +56 \\\Leftrightarrow & -1155x \color{red}{-99} \color{blue}{+99} \color{blue}{-616x} & = & \color{red}{616x} +56 \color{blue}{-616x} \color{blue}{+99} \\\Leftrightarrow & -1155x-616x& = & 56+99 \\\Leftrightarrow & \color{red}{-1771} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-1771} & & \\\Leftrightarrow & x = \frac{-155}{1771} & & \\ & V = \left\{ \frac{-155}{1771} \right\} & \\\end{align}\)