Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+72} & = & \color{red}{308x} +99 \\\Leftrightarrow & 1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & 1320x-308x& = & 99-72 \\\Leftrightarrow & \color{red}{1012} x& = & 27 \\\Leftrightarrow & x = \frac{27}{1012} & & \\ & V = \left\{ \frac{27}{1012} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 9x+\frac{15}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+75} & = & \color{red}{220x} +66 \\\Leftrightarrow & 495x \color{red}{+75} \color{blue}{-75} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{-75} \\\Leftrightarrow & 495x-220x& = & 66-75 \\\Leftrightarrow & \color{red}{275} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{275} & & \\ & V = \left\{ \frac{-9}{275} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{147x} +35 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & -336x-147x& = & 35+48 \\\Leftrightarrow & \color{red}{-483} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-483} & & \\\Leftrightarrow & x = \frac{-83}{483} & & \\ & V = \left\{ \frac{-83}{483} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{11})& = & 8x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{10}{11}& = & 8x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+70} & = & \color{red}{616x} +44 \\\Leftrightarrow & -1155x \color{red}{+70} \color{blue}{-70} \color{blue}{-616x} & = & \color{red}{616x} +44 \color{blue}{-616x} \color{blue}{-70} \\\Leftrightarrow & -1155x-616x& = & 44-70 \\\Leftrightarrow & \color{red}{-1771} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1771} & & \\\Leftrightarrow & x = \frac{26}{1771} & & \\ & V = \left\{ \frac{26}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{9})& = & 3x+\frac{7}{9} \\\Leftrightarrow & -35x+\frac{35}{9}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+35} & = & \color{red}{27x} +7 \\\Leftrightarrow & -315x \color{red}{+35} \color{blue}{-35} \color{blue}{-27x} & = & \color{red}{27x} +7 \color{blue}{-27x} \color{blue}{-35} \\\Leftrightarrow & -315x-27x& = & 7-35 \\\Leftrightarrow & \color{red}{-342} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-342} & & \\\Leftrightarrow & x = \frac{14}{171} & & \\ & V = \left\{ \frac{14}{171} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & 84x+35x& = & 2-30 \\\Leftrightarrow & \color{red}{119} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{119} & & \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -25x-\frac{15}{2}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{-75} & = & \color{red}{40x} +4 \\\Leftrightarrow & -250x \color{red}{-75} \color{blue}{+75} \color{blue}{-40x} & = & \color{red}{40x} +4 \color{blue}{-40x} \color{blue}{+75} \\\Leftrightarrow & -250x-40x& = & 4+75 \\\Leftrightarrow & \color{red}{-290} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-290} & & \\\Leftrightarrow & x = \frac{-79}{290} & & \\ & V = \left\{ \frac{-79}{290} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+126} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 1386x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & 1386x+385x& = & 110-126 \\\Leftrightarrow & \color{red}{1771} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{1771} & & \\ & V = \left\{ \frac{-16}{1771} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{105x} +15 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +15 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 168x-105x& = & 15-28 \\\Leftrightarrow & \color{red}{63} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{63} & & \\ & V = \left\{ \frac{-13}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{4}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{36}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-36} & = & \color{red}{693x} +44 \\\Leftrightarrow & -594x \color{red}{-36} \color{blue}{+36} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+36} \\\Leftrightarrow & -594x-693x& = & 44+36 \\\Leftrightarrow & \color{red}{-1287} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1287} & & \\\Leftrightarrow & x = \frac{-80}{1287} & & \\ & V = \left\{ \frac{-80}{1287} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{10}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-30} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -264x \color{red}{-30} \color{blue}{+30} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{+30} \\\Leftrightarrow & -264x+99x& = & 44+30 \\\Leftrightarrow & \color{red}{-165} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-165} & & \\\Leftrightarrow & x = \frac{-74}{165} & & \\ & V = \left\{ \frac{-74}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{3})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{4}{3}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{16}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-16} & = & \color{red}{-84x} +27 \\\Leftrightarrow & 120x \color{red}{-16} \color{blue}{+16} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{+16} \\\Leftrightarrow & 120x+84x& = & 27+16 \\\Leftrightarrow & \color{red}{204} x& = & 43 \\\Leftrightarrow & x = \frac{43}{204} & & \\ & V = \left\{ \frac{43}{204} \right\} & \\\end{align}\)