Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{+48} & = & \color{red}{-504x} +21 \\\Leftrightarrow & -448x \color{red}{+48} \color{blue}{-48} \color{blue}{+504x} & = & \color{red}{-504x} +21 \color{blue}{+504x} \color{blue}{-48} \\\Leftrightarrow & -448x+504x& = & 21-48 \\\Leftrightarrow & \color{red}{56} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{56} & & \\ & V = \left\{ \frac{-27}{56} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-108} & = & \color{red}{225x} +35 \\\Leftrightarrow & 270x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +35 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & 270x-225x& = & 35+108 \\\Leftrightarrow & \color{red}{45} x& = & 143 \\\Leftrightarrow & x = \frac{143}{45} & & \\ & V = \left\{ \frac{143}{45} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+135} & = & \color{red}{180x} +16 \\\Leftrightarrow & -432x \color{red}{+135} \color{blue}{-135} \color{blue}{-180x} & = & \color{red}{180x} +16 \color{blue}{-180x} \color{blue}{-135} \\\Leftrightarrow & -432x-180x& = & 16-135 \\\Leftrightarrow & \color{red}{-612} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-612} & & \\\Leftrightarrow & x = \frac{7}{36} & & \\ & V = \left\{ \frac{7}{36} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{8})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 20x+\frac{25}{8}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x+ \frac{125}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{+125} & = & \color{red}{-360x} +64 \\\Leftrightarrow & 800x \color{red}{+125} \color{blue}{-125} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{-125} \\\Leftrightarrow & 800x+360x& = & 64-125 \\\Leftrightarrow & \color{red}{1160} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1160} & & \\ & V = \left\{ \frac{-61}{1160} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{6})& = & -2x+\frac{2}{7} \\\Leftrightarrow & 15x+\frac{25}{6}& = & -2x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+175} & = & \color{red}{-84x} +12 \\\Leftrightarrow & 630x \color{red}{+175} \color{blue}{-175} \color{blue}{+84x} & = & \color{red}{-84x} +12 \color{blue}{+84x} \color{blue}{-175} \\\Leftrightarrow & 630x+84x& = & 12-175 \\\Leftrightarrow & \color{red}{714} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{714} & & \\ & V = \left\{ \frac{-163}{714} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -9x+\frac{7}{12} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -9x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{672}{ \color{blue}{84} }x- \frac{240}{ \color{blue}{84} })& = & (\frac{-756}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 672x \color{red}{-240} & = & \color{red}{-756x} +49 \\\Leftrightarrow & 672x \color{red}{-240} \color{blue}{+240} \color{blue}{+756x} & = & \color{red}{-756x} +49 \color{blue}{+756x} \color{blue}{+240} \\\Leftrightarrow & 672x+756x& = & 49+240 \\\Leftrightarrow & \color{red}{1428} x& = & 289 \\\Leftrightarrow & x = \frac{289}{1428} & & \\\Leftrightarrow & x = \frac{17}{84} & & \\ & V = \left\{ \frac{17}{84} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+270} & = & \color{red}{315x} +28 \\\Leftrightarrow & 756x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & 756x-315x& = & 28-270 \\\Leftrightarrow & \color{red}{441} x& = & -242 \\\Leftrightarrow & x = \frac{-242}{441} & & \\ & V = \left\{ \frac{-242}{441} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+90} & = & \color{red}{504x} +70 \\\Leftrightarrow & -945x \color{red}{+90} \color{blue}{-90} \color{blue}{-504x} & = & \color{red}{504x} +70 \color{blue}{-504x} \color{blue}{-90} \\\Leftrightarrow & -945x-504x& = & 70-90 \\\Leftrightarrow & \color{red}{-1449} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-1449} & & \\\Leftrightarrow & x = \frac{20}{1449} & & \\ & V = \left\{ \frac{20}{1449} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{55x} +5 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-30} \\\Leftrightarrow & 198x-55x& = & 5-30 \\\Leftrightarrow & \color{red}{143} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{143} & & \\ & V = \left\{ \frac{-25}{143} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-54} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -594x \color{red}{-54} \color{blue}{+54} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+54} \\\Leftrightarrow & -594x+693x& = & 88+54 \\\Leftrightarrow & \color{red}{99} x& = & 142 \\\Leftrightarrow & x = \frac{142}{99} & & \\ & V = \left\{ \frac{142}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-30} & = & \color{red}{231x} +110 \\\Leftrightarrow & 132x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & 132x-231x& = & 110+30 \\\Leftrightarrow & \color{red}{-99} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-99} & & \\\Leftrightarrow & x = \frac{-140}{99} & & \\ & V = \left\{ \frac{-140}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{135x} +10 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{-12} \\\Leftrightarrow & -120x-135x& = & 10-12 \\\Leftrightarrow & \color{red}{-255} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-255} & & \\\Leftrightarrow & x = \frac{2}{255} & & \\ & V = \left\{ \frac{2}{255} \right\} & \\\end{align}\)