Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{9})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+40} & = & \color{red}{36x} +27 \\\Leftrightarrow & 270x \color{red}{+40} \color{blue}{-40} \color{blue}{-36x} & = & \color{red}{36x} +27 \color{blue}{-36x} \color{blue}{-40} \\\Leftrightarrow & 270x-36x& = & 27-40 \\\Leftrightarrow & \color{red}{234} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{234} & & \\\Leftrightarrow & x = \frac{-1}{18} & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{18x} +21 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & -120x-18x& = & 21+40 \\\Leftrightarrow & \color{red}{-138} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-138} & & \\\Leftrightarrow & x = \frac{-61}{138} & & \\ & V = \left\{ \frac{-61}{138} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{8}{5}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-8} & = & \color{red}{-45x} +8 \\\Leftrightarrow & -40x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & -40x+45x& = & 8+8 \\\Leftrightarrow & \color{red}{5} x& = & 16 \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+45} & = & \color{red}{-84x} +32 \\\Leftrightarrow & 240x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +32 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & 240x+84x& = & 32-45 \\\Leftrightarrow & \color{red}{324} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{324} & & \\ & V = \left\{ \frac{-13}{324} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{-35x} +3 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{+4} \\\Leftrightarrow & -30x+35x& = & 3+4 \\\Leftrightarrow & \color{red}{5} x& = & 7 \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{3})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{-108x} +15 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{+108x} & = & \color{red}{-108x} +15 \color{blue}{+108x} \color{blue}{+32} \\\Leftrightarrow & -96x+108x& = & 15+32 \\\Leftrightarrow & \color{red}{12} x& = & 47 \\\Leftrightarrow & x = \frac{47}{12} & & \\ & V = \left\{ \frac{47}{12} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 9x+\frac{3}{5} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{135x} +9 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{-135x} & = & \color{red}{135x} +9 \color{blue}{-135x} \color{blue}{+70} \\\Leftrightarrow & 420x-135x& = & 9+70 \\\Leftrightarrow & \color{red}{285} x& = & 79 \\\Leftrightarrow & x = \frac{79}{285} & & \\ & V = \left\{ \frac{79}{285} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-32} & = & \color{red}{198x} +99 \\\Leftrightarrow & 440x \color{red}{-32} \color{blue}{+32} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{+32} \\\Leftrightarrow & 440x-198x& = & 99+32 \\\Leftrightarrow & \color{red}{242} x& = & 131 \\\Leftrightarrow & x = \frac{131}{242} & & \\ & V = \left\{ \frac{131}{242} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{105x} +50 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 270x-105x& = & 50+36 \\\Leftrightarrow & \color{red}{165} x& = & 86 \\\Leftrightarrow & x = \frac{86}{165} & & \\ & V = \left\{ \frac{86}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -16x-\frac{8}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-24} & = & \color{red}{63x} +5 \\\Leftrightarrow & -144x \color{red}{-24} \color{blue}{+24} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{+24} \\\Leftrightarrow & -144x-63x& = & 5+24 \\\Leftrightarrow & \color{red}{-207} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-207} & & \\\Leftrightarrow & x = \frac{-29}{207} & & \\ & V = \left\{ \frac{-29}{207} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 8x+\frac{7}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 8x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{320x} +56 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{-320x} & = & \color{red}{320x} +56 \color{blue}{-320x} \color{blue}{+105} \\\Leftrightarrow & 840x-320x& = & 56+105 \\\Leftrightarrow & \color{red}{520} x& = & 161 \\\Leftrightarrow & x = \frac{161}{520} & & \\ & V = \left\{ \frac{161}{520} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{+60} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -700x \color{red}{+60} \color{blue}{-60} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{-60} \\\Leftrightarrow & -700x+490x& = & 49-60 \\\Leftrightarrow & \color{red}{-210} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-210} & & \\\Leftrightarrow & x = \frac{11}{210} & & \\ & V = \left\{ \frac{11}{210} \right\} & \\\end{align}\)