Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -42x+49x& = & 10-6 \\\Leftrightarrow & \color{red}{7} x& = & 4 \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{2})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{25}{2}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-75} & = & \color{red}{-42x} +4 \\\Leftrightarrow & -60x \color{red}{-75} \color{blue}{+75} \color{blue}{+42x} & = & \color{red}{-42x} +4 \color{blue}{+42x} \color{blue}{+75} \\\Leftrightarrow & -60x+42x& = & 4+75 \\\Leftrightarrow & \color{red}{-18} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-18} & & \\\Leftrightarrow & x = \frac{-79}{18} & & \\ & V = \left\{ \frac{-79}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+66} & = & \color{red}{385x} +28 \\\Leftrightarrow & 924x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & 924x-385x& = & 28-66 \\\Leftrightarrow & \color{red}{539} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{539} & & \\ & V = \left\{ \frac{-38}{539} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{12})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -14x+\frac{35}{12}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x+ \frac{105}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+105} & = & \color{red}{108x} +16 \\\Leftrightarrow & -504x \color{red}{+105} \color{blue}{-105} \color{blue}{-108x} & = & \color{red}{108x} +16 \color{blue}{-108x} \color{blue}{-105} \\\Leftrightarrow & -504x-108x& = & 16-105 \\\Leftrightarrow & \color{red}{-612} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-612} & & \\\Leftrightarrow & x = \frac{89}{612} & & \\ & V = \left\{ \frac{89}{612} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+90} & = & \color{red}{-567x} +70 \\\Leftrightarrow & 504x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +70 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & 504x+567x& = & 70-90 \\\Leftrightarrow & \color{red}{1071} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{1071} & & \\ & V = \left\{ \frac{-20}{1071} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{7})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{15}{7}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+45} & = & \color{red}{84x} +70 \\\Leftrightarrow & 315x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +70 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & 315x-84x& = & 70-45 \\\Leftrightarrow & \color{red}{231} x& = & 25 \\\Leftrightarrow & x = \frac{25}{231} & & \\ & V = \left\{ \frac{25}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -126x-147x& = & 56-30 \\\Leftrightarrow & \color{red}{-273} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-273} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +20 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 20+132 \\\Leftrightarrow & \color{red}{-935} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-935} & & \\\Leftrightarrow & x = \frac{-152}{935} & & \\ & V = \left\{ \frac{-152}{935} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{896}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 896x \color{red}{-160} & = & \color{red}{-392x} +35 \\\Leftrightarrow & 896x \color{red}{-160} \color{blue}{+160} \color{blue}{+392x} & = & \color{red}{-392x} +35 \color{blue}{+392x} \color{blue}{+160} \\\Leftrightarrow & 896x+392x& = & 35+160 \\\Leftrightarrow & \color{red}{1288} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1288} & & \\ & V = \left\{ \frac{195}{1288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+36} \\\Leftrightarrow & 660x+231x& = & 88+36 \\\Leftrightarrow & \color{red}{891} x& = & 124 \\\Leftrightarrow & x = \frac{124}{891} & & \\ & V = \left\{ \frac{124}{891} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{270x} +27 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+175} \\\Leftrightarrow & 420x-270x& = & 27+175 \\\Leftrightarrow & \color{red}{150} x& = & 202 \\\Leftrightarrow & x = \frac{202}{150} & & \\\Leftrightarrow & x = \frac{101}{75} & & \\ & V = \left\{ \frac{101}{75} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 28x+4& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{196}{ \color{blue}{7} }x+ \frac{28}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 196x \color{red}{+28} & = & \color{red}{35x} +2 \\\Leftrightarrow & 196x \color{red}{+28} \color{blue}{-28} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-28} \\\Leftrightarrow & 196x-35x& = & 2-28 \\\Leftrightarrow & \color{red}{161} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{161} & & \\ & V = \left\{ \frac{-26}{161} \right\} & \\\end{align}\)