Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-108} & = & \color{red}{315x} +56 \\\Leftrightarrow & 756x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & 756x-315x& = & 56+108 \\\Leftrightarrow & \color{red}{441} x& = & 164 \\\Leftrightarrow & x = \frac{164}{441} & & \\ & V = \left\{ \frac{164}{441} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+54} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 540x \color{red}{+54} \color{blue}{-54} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-54} \\\Leftrightarrow & 540x+225x& = & 50-54 \\\Leftrightarrow & \color{red}{765} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{765} & & \\ & V = \left\{ \frac{-4}{765} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 9x+\frac{9}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+45} & = & \color{red}{220x} +66 \\\Leftrightarrow & 495x \color{red}{+45} \color{blue}{-45} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{-45} \\\Leftrightarrow & 495x-220x& = & 66-45 \\\Leftrightarrow & \color{red}{275} x& = & 21 \\\Leftrightarrow & x = \frac{21}{275} & & \\ & V = \left\{ \frac{21}{275} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{45x} +12 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-100} \\\Leftrightarrow & 240x-45x& = & 12-100 \\\Leftrightarrow & \color{red}{195} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{195} & & \\ & V = \left\{ \frac{-88}{195} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-45x} +2 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{+28} \\\Leftrightarrow & -252x+45x& = & 2+28 \\\Leftrightarrow & \color{red}{-207} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-207} & & \\\Leftrightarrow & x = \frac{-10}{69} & & \\ & V = \left\{ \frac{-10}{69} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -420x+175x& = & 10-84 \\\Leftrightarrow & \color{red}{-245} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-245} & & \\\Leftrightarrow & x = \frac{74}{245} & & \\ & V = \left\{ \frac{74}{245} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -4x+\frac{9}{7} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+140} & = & \color{red}{-84x} +27 \\\Leftrightarrow & -525x \color{red}{+140} \color{blue}{-140} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{-140} \\\Leftrightarrow & -525x+84x& = & 27-140 \\\Leftrightarrow & \color{red}{-441} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-441} & & \\\Leftrightarrow & x = \frac{113}{441} & & \\ & V = \left\{ \frac{113}{441} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{4})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{25}{4}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{75}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-75} & = & \color{red}{-96x} +8 \\\Leftrightarrow & -180x \color{red}{-75} \color{blue}{+75} \color{blue}{+96x} & = & \color{red}{-96x} +8 \color{blue}{+96x} \color{blue}{+75} \\\Leftrightarrow & -180x+96x& = & 8+75 \\\Leftrightarrow & \color{red}{-84} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-84} & & \\\Leftrightarrow & x = \frac{-83}{84} & & \\ & V = \left\{ \frac{-83}{84} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{8})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -35x+\frac{35}{8}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x+ \frac{245}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{+245} & = & \color{red}{-504x} +24 \\\Leftrightarrow & -1960x \color{red}{+245} \color{blue}{-245} \color{blue}{+504x} & = & \color{red}{-504x} +24 \color{blue}{+504x} \color{blue}{-245} \\\Leftrightarrow & -1960x+504x& = & 24-245 \\\Leftrightarrow & \color{red}{-1456} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-1456} & & \\\Leftrightarrow & x = \frac{17}{112} & & \\ & V = \left\{ \frac{17}{112} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{9})& = & 8x+\frac{4}{11} \\\Leftrightarrow & -21x-\frac{35}{9}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{-385} & = & \color{red}{792x} +36 \\\Leftrightarrow & -2079x \color{red}{-385} \color{blue}{+385} \color{blue}{-792x} & = & \color{red}{792x} +36 \color{blue}{-792x} \color{blue}{+385} \\\Leftrightarrow & -2079x-792x& = & 36+385 \\\Leftrightarrow & \color{red}{-2871} x& = & 421 \\\Leftrightarrow & x = \frac{421}{-2871} & & \\\Leftrightarrow & x = \frac{-421}{2871} & & \\ & V = \left\{ \frac{-421}{2871} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & 9x+\frac{7}{4} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 9x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{288}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 288x \color{red}{+32} & = & \color{red}{324x} +63 \\\Leftrightarrow & 288x \color{red}{+32} \color{blue}{-32} \color{blue}{-324x} & = & \color{red}{324x} +63 \color{blue}{-324x} \color{blue}{-32} \\\Leftrightarrow & 288x-324x& = & 63-32 \\\Leftrightarrow & \color{red}{-36} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-36} & & \\\Leftrightarrow & x = \frac{-31}{36} & & \\ & V = \left\{ \frac{-31}{36} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{25x} +8 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & 90x-25x& = & 8+18 \\\Leftrightarrow & \color{red}{65} x& = & 26 \\\Leftrightarrow & x = \frac{26}{65} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)