Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{-595} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-595} & & \\\Leftrightarrow & x = \frac{108}{595} & & \\ & V = \left\{ \frac{108}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{11})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{10}{11}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-90} & = & \color{red}{-693x} +44 \\\Leftrightarrow & 1980x \color{red}{-90} \color{blue}{+90} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{+90} \\\Leftrightarrow & 1980x+693x& = & 44+90 \\\Leftrightarrow & \color{red}{2673} x& = & 134 \\\Leftrightarrow & x = \frac{134}{2673} & & \\ & V = \left\{ \frac{134}{2673} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1120}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1120x \color{red}{+160} & = & \color{red}{350x} +21 \\\Leftrightarrow & 1120x \color{red}{+160} \color{blue}{-160} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{-160} \\\Leftrightarrow & 1120x-350x& = & 21-160 \\\Leftrightarrow & \color{red}{770} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{770} & & \\ & V = \left\{ \frac{-139}{770} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-75} & = & \color{red}{200x} +48 \\\Leftrightarrow & 480x \color{red}{-75} \color{blue}{+75} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{+75} \\\Leftrightarrow & 480x-200x& = & 48+75 \\\Leftrightarrow & \color{red}{280} x& = & 123 \\\Leftrightarrow & x = \frac{123}{280} & & \\ & V = \left\{ \frac{123}{280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{84}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+84} & = & \color{red}{120x} +40 \\\Leftrightarrow & 315x \color{red}{+84} \color{blue}{-84} \color{blue}{-120x} & = & \color{red}{120x} +40 \color{blue}{-120x} \color{blue}{-84} \\\Leftrightarrow & 315x-120x& = & 40-84 \\\Leftrightarrow & \color{red}{195} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{195} & & \\ & V = \left\{ \frac{-44}{195} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+18} & = & \color{red}{55x} +8 \\\Leftrightarrow & 198x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 198x-55x& = & 8-18 \\\Leftrightarrow & \color{red}{143} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{143} & & \\ & V = \left\{ \frac{-10}{143} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{2})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{9}{2}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-63} & = & \color{red}{98x} +12 \\\Leftrightarrow & 84x \color{red}{-63} \color{blue}{+63} \color{blue}{-98x} & = & \color{red}{98x} +12 \color{blue}{-98x} \color{blue}{+63} \\\Leftrightarrow & 84x-98x& = & 12+63 \\\Leftrightarrow & \color{red}{-14} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-14} & & \\\Leftrightarrow & x = \frac{-75}{14} & & \\ & V = \left\{ \frac{-75}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{28x} +18 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +18 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -24x-28x& = & 18+15 \\\Leftrightarrow & \color{red}{-52} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-52} & & \\\Leftrightarrow & x = \frac{-33}{52} & & \\ & V = \left\{ \frac{-33}{52} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-100} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -120x \color{red}{-100} \color{blue}{+100} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+100} \\\Leftrightarrow & -120x+45x& = & 6+100 \\\Leftrightarrow & \color{red}{-75} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-75} & & \\\Leftrightarrow & x = \frac{-106}{75} & & \\ & V = \left\{ \frac{-106}{75} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{10})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 6x+\frac{9}{10}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{+99} & = & \color{red}{550x} +100 \\\Leftrightarrow & 660x \color{red}{+99} \color{blue}{-99} \color{blue}{-550x} & = & \color{red}{550x} +100 \color{blue}{-550x} \color{blue}{-99} \\\Leftrightarrow & 660x-550x& = & 100-99 \\\Leftrightarrow & \color{red}{110} x& = & 1 \\\Leftrightarrow & x = \frac{1}{110} & & \\ & V = \left\{ \frac{1}{110} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{4})& = & 2x+\frac{5}{4} \\\Leftrightarrow & -25x+\frac{25}{4}& = & 2x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x+ \frac{25}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{+25} & = & \color{red}{8x} +5 \\\Leftrightarrow & -100x \color{red}{+25} \color{blue}{-25} \color{blue}{-8x} & = & \color{red}{8x} +5 \color{blue}{-8x} \color{blue}{-25} \\\Leftrightarrow & -100x-8x& = & 5-25 \\\Leftrightarrow & \color{red}{-108} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-108} & & \\\Leftrightarrow & x = \frac{5}{27} & & \\ & V = \left\{ \frac{5}{27} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{20}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-100} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -450x \color{red}{-100} \color{blue}{+100} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+100} \\\Leftrightarrow & -450x+315x& = & 54+100 \\\Leftrightarrow & \color{red}{-135} x& = & 154 \\\Leftrightarrow & x = \frac{154}{-135} & & \\\Leftrightarrow & x = \frac{-154}{135} & & \\ & V = \left\{ \frac{-154}{135} \right\} & \\\end{align}\)