Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & -168x+35x& = & 8-30 \\\Leftrightarrow & \color{red}{-133} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-133} & & \\\Leftrightarrow & x = \frac{22}{133} & & \\ & V = \left\{ \frac{22}{133} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{6}{11}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{693x} +22 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{+54} \\\Leftrightarrow & -990x-693x& = & 22+54 \\\Leftrightarrow & \color{red}{-1683} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-1683} & & \\\Leftrightarrow & x = \frac{-76}{1683} & & \\ & V = \left\{ \frac{-76}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 14x-\frac{21}{2}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{56}{ \color{blue}{4} }x- \frac{42}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 56x \color{red}{-42} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 56x \color{red}{-42} \color{blue}{+42} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{+42} \\\Leftrightarrow & 56x+12x& = & 9+42 \\\Leftrightarrow & \color{red}{68} x& = & 51 \\\Leftrightarrow & x = \frac{51}{68} & & \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+28} & = & \color{red}{-90x} +35 \\\Leftrightarrow & 140x \color{red}{+28} \color{blue}{-28} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{-28} \\\Leftrightarrow & 140x+90x& = & 35-28 \\\Leftrightarrow & \color{red}{230} x& = & 7 \\\Leftrightarrow & x = \frac{7}{230} & & \\ & V = \left\{ \frac{7}{230} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{-300x} +35 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{+300x} & = & \color{red}{-300x} +35 \color{blue}{+300x} \color{blue}{-144} \\\Leftrightarrow & 720x+300x& = & 35-144 \\\Leftrightarrow & \color{red}{1020} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1020} & & \\ & V = \left\{ \frac{-109}{1020} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{12}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-60} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1100x \color{red}{-60} \color{blue}{+60} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+60} \\\Leftrightarrow & -1100x-385x& = & 66+60 \\\Leftrightarrow & \color{red}{-1485} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-1485} & & \\\Leftrightarrow & x = \frac{-14}{165} & & \\ & V = \left\{ \frac{-14}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{98x} +63 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+40} \\\Leftrightarrow & -280x-98x& = & 63+40 \\\Leftrightarrow & \color{red}{-378} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-378} & & \\\Leftrightarrow & x = \frac{-103}{378} & & \\ & V = \left\{ \frac{-103}{378} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{7})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{-63x} +49 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{+63x} & = & \color{red}{-63x} +49 \color{blue}{+63x} \color{blue}{+18} \\\Leftrightarrow & 84x+63x& = & 49+18 \\\Leftrightarrow & \color{red}{147} x& = & 67 \\\Leftrightarrow & x = \frac{67}{147} & & \\ & V = \left\{ \frac{67}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{4}{3}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{-4} & = & \color{red}{15x} +2 \\\Leftrightarrow & 18x \color{red}{-4} \color{blue}{+4} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{+4} \\\Leftrightarrow & 18x-15x& = & 2+4 \\\Leftrightarrow & \color{red}{3} x& = & 6 \\\Leftrightarrow & x = \frac{6}{3} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{9})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{-297x} +90 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +90 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & -792x+297x& = & 90-88 \\\Leftrightarrow & \color{red}{-495} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-495} & & \\\Leftrightarrow & x = \frac{-2}{495} & & \\ & V = \left\{ \frac{-2}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+56} & = & \color{red}{189x} +30 \\\Leftrightarrow & -84x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -84x-189x& = & 30-56 \\\Leftrightarrow & \color{red}{-273} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-273} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{9})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -35x-\frac{14}{9}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1260}{ \color{blue}{36} }x- \frac{56}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1260x \color{red}{-56} & = & \color{red}{108x} +21 \\\Leftrightarrow & -1260x \color{red}{-56} \color{blue}{+56} \color{blue}{-108x} & = & \color{red}{108x} +21 \color{blue}{-108x} \color{blue}{+56} \\\Leftrightarrow & -1260x-108x& = & 21+56 \\\Leftrightarrow & \color{red}{-1368} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-1368} & & \\\Leftrightarrow & x = \frac{-77}{1368} & & \\ & V = \left\{ \frac{-77}{1368} \right\} & \\\end{align}\)