Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{9})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{16}{9}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{112}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-112} & = & \color{red}{-441x} +54 \\\Leftrightarrow & 504x \color{red}{-112} \color{blue}{+112} \color{blue}{+441x} & = & \color{red}{-441x} +54 \color{blue}{+441x} \color{blue}{+112} \\\Leftrightarrow & 504x+441x& = & 54+112 \\\Leftrightarrow & \color{red}{945} x& = & 166 \\\Leftrightarrow & x = \frac{166}{945} & & \\ & V = \left\{ \frac{166}{945} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+84} & = & \color{red}{105x} +20 \\\Leftrightarrow & -630x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & -630x-105x& = & 20-84 \\\Leftrightarrow & \color{red}{-735} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-735} & & \\\Leftrightarrow & x = \frac{64}{735} & & \\ & V = \left\{ \frac{64}{735} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{1}{2})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -28x-\frac{7}{2}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-56}{ \color{blue}{2} }x- \frac{7}{ \color{blue}{2} })& = & (\frac{18}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -56x \color{red}{-7} & = & \color{red}{18x} +9 \\\Leftrightarrow & -56x \color{red}{-7} \color{blue}{+7} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+7} \\\Leftrightarrow & -56x-18x& = & 9+7 \\\Leftrightarrow & \color{red}{-74} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-74} & & \\\Leftrightarrow & x = \frac{-8}{37} & & \\ & V = \left\{ \frac{-8}{37} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+36} & = & \color{red}{126x} +35 \\\Leftrightarrow & -336x \color{red}{+36} \color{blue}{-36} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-36} \\\Leftrightarrow & -336x-126x& = & 35-36 \\\Leftrightarrow & \color{red}{-462} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-462} & & \\\Leftrightarrow & x = \frac{1}{462} & & \\ & V = \left\{ \frac{1}{462} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{11})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x-\frac{15}{11}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-15} & = & \color{red}{-55x} +9 \\\Leftrightarrow & -132x \color{red}{-15} \color{blue}{+15} \color{blue}{+55x} & = & \color{red}{-55x} +9 \color{blue}{+55x} \color{blue}{+15} \\\Leftrightarrow & -132x+55x& = & 9+15 \\\Leftrightarrow & \color{red}{-77} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-77} & & \\\Leftrightarrow & x = \frac{-24}{77} & & \\ & V = \left\{ \frac{-24}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 6x+\frac{9}{5}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{54}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+54} & = & \color{red}{150x} +35 \\\Leftrightarrow & 180x \color{red}{+54} \color{blue}{-54} \color{blue}{-150x} & = & \color{red}{150x} +35 \color{blue}{-150x} \color{blue}{-54} \\\Leftrightarrow & 180x-150x& = & 35-54 \\\Leftrightarrow & \color{red}{30} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{30} & & \\ & V = \left\{ \frac{-19}{30} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{6}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-54} & = & \color{red}{-495x} +110 \\\Leftrightarrow & 1188x \color{red}{-54} \color{blue}{+54} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{+54} \\\Leftrightarrow & 1188x+495x& = & 110+54 \\\Leftrightarrow & \color{red}{1683} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1683} & & \\ & V = \left\{ \frac{164}{1683} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-6} & = & \color{red}{-49x} +3 \\\Leftrightarrow & 84x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & 84x+49x& = & 3+6 \\\Leftrightarrow & \color{red}{133} x& = & 9 \\\Leftrightarrow & x = \frac{9}{133} & & \\ & V = \left\{ \frac{9}{133} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{9})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{20}{9}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{-126x} +45 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{+40} \\\Leftrightarrow & -180x+126x& = & 45+40 \\\Leftrightarrow & \color{red}{-54} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-54} & & \\\Leftrightarrow & x = \frac{-85}{54} & & \\ & V = \left\{ \frac{-85}{54} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{-15} & = & \color{red}{12x} +10 \\\Leftrightarrow & 40x \color{red}{-15} \color{blue}{+15} \color{blue}{-12x} & = & \color{red}{12x} +10 \color{blue}{-12x} \color{blue}{+15} \\\Leftrightarrow & 40x-12x& = & 10+15 \\\Leftrightarrow & \color{red}{28} x& = & 25 \\\Leftrightarrow & x = \frac{25}{28} & & \\ & V = \left\{ \frac{25}{28} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{-30x} +40 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{+30x} & = & \color{red}{-30x} +40 \color{blue}{+30x} \color{blue}{-36} \\\Leftrightarrow & 135x+30x& = & 40-36 \\\Leftrightarrow & \color{red}{165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{165} & & \\ & V = \left\{ \frac{4}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 6x+\frac{9}{5}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+72} & = & \color{red}{-200x} +25 \\\Leftrightarrow & 240x \color{red}{+72} \color{blue}{-72} \color{blue}{+200x} & = & \color{red}{-200x} +25 \color{blue}{+200x} \color{blue}{-72} \\\Leftrightarrow & 240x+200x& = & 25-72 \\\Leftrightarrow & \color{red}{440} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{440} & & \\ & V = \left\{ \frac{-47}{440} \right\} & \\\end{align}\)