Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{6})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -14x+\frac{35}{6}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-588}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-126}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -588x \color{red}{+245} & = & \color{red}{-126x} +48 \\\Leftrightarrow & -588x \color{red}{+245} \color{blue}{-245} \color{blue}{+126x} & = & \color{red}{-126x} +48 \color{blue}{+126x} \color{blue}{-245} \\\Leftrightarrow & -588x+126x& = & 48-245 \\\Leftrightarrow & \color{red}{-462} x& = & -197 \\\Leftrightarrow & x = \frac{-197}{-462} & & \\\Leftrightarrow & x = \frac{197}{462} & & \\ & V = \left\{ \frac{197}{462} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x+ \frac{108}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{+108} & = & \color{red}{-300x} +25 \\\Leftrightarrow & -720x \color{red}{+108} \color{blue}{-108} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{-108} \\\Leftrightarrow & -720x+300x& = & 25-108 \\\Leftrightarrow & \color{red}{-420} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-420} & & \\\Leftrightarrow & x = \frac{83}{420} & & \\ & V = \left\{ \frac{83}{420} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{8})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x+\frac{15}{8}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{392x} +32 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{-392x} & = & \color{red}{392x} +32 \color{blue}{-392x} \color{blue}{-105} \\\Leftrightarrow & -560x-392x& = & 32-105 \\\Leftrightarrow & \color{red}{-952} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-952} & & \\\Leftrightarrow & x = \frac{73}{952} & & \\ & V = \left\{ \frac{73}{952} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & -9x+\frac{5}{12} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x+ \frac{112}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{+112} & = & \color{red}{-324x} +15 \\\Leftrightarrow & 1008x \color{red}{+112} \color{blue}{-112} \color{blue}{+324x} & = & \color{red}{-324x} +15 \color{blue}{+324x} \color{blue}{-112} \\\Leftrightarrow & 1008x+324x& = & 15-112 \\\Leftrightarrow & \color{red}{1332} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{1332} & & \\ & V = \left\{ \frac{-97}{1332} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{4})& = & -2x+\frac{5}{2} \\\Leftrightarrow & 9x-\frac{9}{4}& = & -2x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{36}{ \color{blue}{4} }x- \frac{9}{ \color{blue}{4} })& = & (\frac{-8}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 36x \color{red}{-9} & = & \color{red}{-8x} +10 \\\Leftrightarrow & 36x \color{red}{-9} \color{blue}{+9} \color{blue}{+8x} & = & \color{red}{-8x} +10 \color{blue}{+8x} \color{blue}{+9} \\\Leftrightarrow & 36x+8x& = & 10+9 \\\Leftrightarrow & \color{red}{44} x& = & 19 \\\Leftrightarrow & x = \frac{19}{44} & & \\ & V = \left\{ \frac{19}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-48} & = & \color{red}{-280x} +49 \\\Leftrightarrow & -672x \color{red}{-48} \color{blue}{+48} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{+48} \\\Leftrightarrow & -672x+280x& = & 49+48 \\\Leftrightarrow & \color{red}{-392} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-392} & & \\\Leftrightarrow & x = \frac{-97}{392} & & \\ & V = \left\{ \frac{-97}{392} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{160x} +24 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{-160x} & = & \color{red}{160x} +24 \color{blue}{-160x} \color{blue}{-75} \\\Leftrightarrow & -300x-160x& = & 24-75 \\\Leftrightarrow & \color{red}{-460} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-460} & & \\\Leftrightarrow & x = \frac{51}{460} & & \\ & V = \left\{ \frac{51}{460} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+54} \\\Leftrightarrow & 270x-75x& = & 20+54 \\\Leftrightarrow & \color{red}{195} x& = & 74 \\\Leftrightarrow & x = \frac{74}{195} & & \\ & V = \left\{ \frac{74}{195} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{7})& = & 9x+\frac{5}{12} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-672}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -672x \color{red}{+120} & = & \color{red}{756x} +35 \\\Leftrightarrow & -672x \color{red}{+120} \color{blue}{-120} \color{blue}{-756x} & = & \color{red}{756x} +35 \color{blue}{-756x} \color{blue}{-120} \\\Leftrightarrow & -672x-756x& = & 35-120 \\\Leftrightarrow & \color{red}{-1428} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-1428} & & \\\Leftrightarrow & x = \frac{5}{84} & & \\ & V = \left\{ \frac{5}{84} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{3})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{28}{3}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+28} & = & \color{red}{6x} +2 \\\Leftrightarrow & 105x \color{red}{+28} \color{blue}{-28} \color{blue}{-6x} & = & \color{red}{6x} +2 \color{blue}{-6x} \color{blue}{-28} \\\Leftrightarrow & 105x-6x& = & 2-28 \\\Leftrightarrow & \color{red}{99} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{99} & & \\ & V = \left\{ \frac{-26}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+1)& = & -3x+\frac{4}{9} \\\Leftrightarrow & -25x-5& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x- \frac{45}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{-45} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -225x \color{red}{-45} \color{blue}{+45} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+45} \\\Leftrightarrow & -225x+27x& = & 4+45 \\\Leftrightarrow & \color{red}{-198} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-198} & & \\\Leftrightarrow & x = \frac{-49}{198} & & \\ & V = \left\{ \frac{-49}{198} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+88} & = & \color{red}{-297x} +15 \\\Leftrightarrow & 528x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & 528x+297x& = & 15-88 \\\Leftrightarrow & \color{red}{825} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{825} & & \\ & V = \left\{ \frac{-73}{825} \right\} & \\\end{align}\)