Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{11})& = & -8x+\frac{9}{8} \\\Leftrightarrow & -21x+\frac{35}{11}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{+280} & = & \color{red}{-704x} +99 \\\Leftrightarrow & -1848x \color{red}{+280} \color{blue}{-280} \color{blue}{+704x} & = & \color{red}{-704x} +99 \color{blue}{+704x} \color{blue}{-280} \\\Leftrightarrow & -1848x+704x& = & 99-280 \\\Leftrightarrow & \color{red}{-1144} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{-1144} & & \\\Leftrightarrow & x = \frac{181}{1144} & & \\ & V = \left\{ \frac{181}{1144} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{8})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{-63} & = & \color{red}{192x} +80 \\\Leftrightarrow & -504x \color{red}{-63} \color{blue}{+63} \color{blue}{-192x} & = & \color{red}{192x} +80 \color{blue}{-192x} \color{blue}{+63} \\\Leftrightarrow & -504x-192x& = & 80+63 \\\Leftrightarrow & \color{red}{-696} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-696} & & \\\Leftrightarrow & x = \frac{-143}{696} & & \\ & V = \left\{ \frac{-143}{696} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{7})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{20}{7}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+20} & = & \color{red}{-14x} +10 \\\Leftrightarrow & 105x \color{red}{+20} \color{blue}{-20} \color{blue}{+14x} & = & \color{red}{-14x} +10 \color{blue}{+14x} \color{blue}{-20} \\\Leftrightarrow & 105x+14x& = & 10-20 \\\Leftrightarrow & \color{red}{119} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{119} & & \\ & V = \left\{ \frac{-10}{119} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{2})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{9}{2}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{45}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-45} & = & \color{red}{40x} +12 \\\Leftrightarrow & 90x \color{red}{-45} \color{blue}{+45} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{+45} \\\Leftrightarrow & 90x-40x& = & 12+45 \\\Leftrightarrow & \color{red}{50} x& = & 57 \\\Leftrightarrow & x = \frac{57}{50} & & \\ & V = \left\{ \frac{57}{50} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{9}{5}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+9} & = & \color{red}{-20x} +6 \\\Leftrightarrow & -75x \color{red}{+9} \color{blue}{-9} \color{blue}{+20x} & = & \color{red}{-20x} +6 \color{blue}{+20x} \color{blue}{-9} \\\Leftrightarrow & -75x+20x& = & 6-9 \\\Leftrightarrow & \color{red}{-55} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-55} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & -630x+441x& = & 14+90 \\\Leftrightarrow & \color{red}{-189} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-189} & & \\\Leftrightarrow & x = \frac{-104}{189} & & \\ & V = \left\{ \frac{-104}{189} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 4x-\frac{6}{11}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{176}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 176x \color{red}{-24} & = & \color{red}{132x} +99 \\\Leftrightarrow & 176x \color{red}{-24} \color{blue}{+24} \color{blue}{-132x} & = & \color{red}{132x} +99 \color{blue}{-132x} \color{blue}{+24} \\\Leftrightarrow & 176x-132x& = & 99+24 \\\Leftrightarrow & \color{red}{44} x& = & 123 \\\Leftrightarrow & x = \frac{123}{44} & & \\ & V = \left\{ \frac{123}{44} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{10})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{9}{10}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{40}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{+63} & = & \color{red}{350x} +40 \\\Leftrightarrow & 840x \color{red}{+63} \color{blue}{-63} \color{blue}{-350x} & = & \color{red}{350x} +40 \color{blue}{-350x} \color{blue}{-63} \\\Leftrightarrow & 840x-350x& = & 40-63 \\\Leftrightarrow & \color{red}{490} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{490} & & \\ & V = \left\{ \frac{-23}{490} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{9})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{28}{9}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-28} & = & \color{red}{-72x} +24 \\\Leftrightarrow & -189x \color{red}{-28} \color{blue}{+28} \color{blue}{+72x} & = & \color{red}{-72x} +24 \color{blue}{+72x} \color{blue}{+28} \\\Leftrightarrow & -189x+72x& = & 24+28 \\\Leftrightarrow & \color{red}{-117} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-117} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-63} & = & \color{red}{-72x} +80 \\\Leftrightarrow & 672x \color{red}{-63} \color{blue}{+63} \color{blue}{+72x} & = & \color{red}{-72x} +80 \color{blue}{+72x} \color{blue}{+63} \\\Leftrightarrow & 672x+72x& = & 80+63 \\\Leftrightarrow & \color{red}{744} x& = & 143 \\\Leftrightarrow & x = \frac{143}{744} & & \\ & V = \left\{ \frac{143}{744} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -28x+\frac{28}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x+ \frac{308}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{+308} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -1540x \color{red}{+308} \color{blue}{-308} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{-308} \\\Leftrightarrow & -1540x+220x& = & 30-308 \\\Leftrightarrow & \color{red}{-1320} x& = & -278 \\\Leftrightarrow & x = \frac{-278}{-1320} & & \\\Leftrightarrow & x = \frac{139}{660} & & \\ & V = \left\{ \frac{139}{660} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{72x} +32 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +32 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & 336x-72x& = & 32-63 \\\Leftrightarrow & \color{red}{264} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{264} & & \\ & V = \left\{ \frac{-31}{264} \right\} & \\\end{align}\)