Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +9 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 9-24 \\\Leftrightarrow & \color{red}{70} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{70} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 126x-105x& = & 70-18 \\\Leftrightarrow & \color{red}{21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{6}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-66} & = & \color{red}{385x} +30 \\\Leftrightarrow & 440x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & 440x-385x& = & 30+66 \\\Leftrightarrow & \color{red}{55} x& = & 96 \\\Leftrightarrow & x = \frac{96}{55} & & \\ & V = \left\{ \frac{96}{55} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 4x+\frac{6}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+18} & = & \color{red}{105x} +10 \\\Leftrightarrow & 60x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 60x-105x& = & 10-18 \\\Leftrightarrow & \color{red}{-45} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-45} & & \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-756}{ \color{blue}{36} }x- \frac{56}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -756x \color{red}{-56} & = & \color{red}{288x} +81 \\\Leftrightarrow & -756x \color{red}{-56} \color{blue}{+56} \color{blue}{-288x} & = & \color{red}{288x} +81 \color{blue}{-288x} \color{blue}{+56} \\\Leftrightarrow & -756x-288x& = & 81+56 \\\Leftrightarrow & \color{red}{-1044} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-1044} & & \\\Leftrightarrow & x = \frac{-137}{1044} & & \\ & V = \left\{ \frac{-137}{1044} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{49x} +9 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{+30} \\\Leftrightarrow & 84x-49x& = & 9+30 \\\Leftrightarrow & \color{red}{35} x& = & 39 \\\Leftrightarrow & x = \frac{39}{35} & & \\ & V = \left\{ \frac{39}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 24x-\frac{12}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-12} & = & \color{red}{35x} +3 \\\Leftrightarrow & 168x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 168x-35x& = & 3+12 \\\Leftrightarrow & \color{red}{133} x& = & 15 \\\Leftrightarrow & x = \frac{15}{133} & & \\ & V = \left\{ \frac{15}{133} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{4}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-4} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+4} \\\Leftrightarrow & -12x+15x& = & 4+4 \\\Leftrightarrow & \color{red}{3} x& = & 8 \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -14x-\frac{14}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x- \frac{126}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{-126} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1386x \color{red}{-126} \color{blue}{+126} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+126} \\\Leftrightarrow & -1386x-495x& = & 88+126 \\\Leftrightarrow & \color{red}{-1881} x& = & 214 \\\Leftrightarrow & x = \frac{214}{-1881} & & \\\Leftrightarrow & x = \frac{-214}{1881} & & \\ & V = \left\{ \frac{-214}{1881} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-50} & = & \color{red}{440x} +33 \\\Leftrightarrow & -825x \color{red}{-50} \color{blue}{+50} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{+50} \\\Leftrightarrow & -825x-440x& = & 33+50 \\\Leftrightarrow & \color{red}{-1265} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-1265} & & \\\Leftrightarrow & x = \frac{-83}{1265} & & \\ & V = \left\{ \frac{-83}{1265} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-60} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 168x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & 168x+98x& = & 49+60 \\\Leftrightarrow & \color{red}{266} x& = & 109 \\\Leftrightarrow & x = \frac{109}{266} & & \\ & V = \left\{ \frac{109}{266} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+176} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 1540x \color{red}{+176} \color{blue}{-176} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{-176} \\\Leftrightarrow & 1540x+693x& = & 42-176 \\\Leftrightarrow & \color{red}{2233} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{2233} & & \\ & V = \left\{ \frac{-134}{2233} \right\} & \\\end{align}\)