Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{11})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x+\frac{8}{11}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+56} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -924x \color{red}{+56} \color{blue}{-56} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-56} \\\Leftrightarrow & -924x+385x& = & 66-56 \\\Leftrightarrow & \color{red}{-539} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-539} & & \\\Leftrightarrow & x = \frac{-10}{539} & & \\ & V = \left\{ \frac{-10}{539} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-144} & = & \color{red}{315x} +56 \\\Leftrightarrow & -756x \color{red}{-144} \color{blue}{+144} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+144} \\\Leftrightarrow & -756x-315x& = & 56+144 \\\Leftrightarrow & \color{red}{-1071} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1071} & & \\\Leftrightarrow & x = \frac{-200}{1071} & & \\ & V = \left\{ \frac{-200}{1071} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{9})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x+\frac{10}{9}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+110} & = & \color{red}{495x} +72 \\\Leftrightarrow & 594x \color{red}{+110} \color{blue}{-110} \color{blue}{-495x} & = & \color{red}{495x} +72 \color{blue}{-495x} \color{blue}{-110} \\\Leftrightarrow & 594x-495x& = & 72-110 \\\Leftrightarrow & \color{red}{99} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{99} & & \\ & V = \left\{ \frac{-38}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-80} & = & \color{red}{-210x} +9 \\\Leftrightarrow & 300x \color{red}{-80} \color{blue}{+80} \color{blue}{+210x} & = & \color{red}{-210x} +9 \color{blue}{+210x} \color{blue}{+80} \\\Leftrightarrow & 300x+210x& = & 9+80 \\\Leftrightarrow & \color{red}{510} x& = & 89 \\\Leftrightarrow & x = \frac{89}{510} & & \\ & V = \left\{ \frac{89}{510} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-48} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -168x \color{red}{-48} \color{blue}{+48} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{+48} \\\Leftrightarrow & -168x+63x& = & 56+48 \\\Leftrightarrow & \color{red}{-105} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-105} & & \\\Leftrightarrow & x = \frac{-104}{105} & & \\ & V = \left\{ \frac{-104}{105} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{8})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+63} & = & \color{red}{-192x} +16 \\\Leftrightarrow & -504x \color{red}{+63} \color{blue}{-63} \color{blue}{+192x} & = & \color{red}{-192x} +16 \color{blue}{+192x} \color{blue}{-63} \\\Leftrightarrow & -504x+192x& = & 16-63 \\\Leftrightarrow & \color{red}{-312} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-312} & & \\\Leftrightarrow & x = \frac{47}{312} & & \\ & V = \left\{ \frac{47}{312} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{11})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x-\frac{10}{11}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-10} & = & \color{red}{-99x} +10 \\\Leftrightarrow & -88x \color{red}{-10} \color{blue}{+10} \color{blue}{+99x} & = & \color{red}{-99x} +10 \color{blue}{+99x} \color{blue}{+10} \\\Leftrightarrow & -88x+99x& = & 10+10 \\\Leftrightarrow & \color{red}{11} x& = & 20 \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & 2x+\frac{4}{7} \\\Leftrightarrow & 21x+\frac{14}{5}& = & 2x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{70x} +20 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{-70x} & = & \color{red}{70x} +20 \color{blue}{-70x} \color{blue}{-98} \\\Leftrightarrow & 735x-70x& = & 20-98 \\\Leftrightarrow & \color{red}{665} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{665} & & \\ & V = \left\{ \frac{-78}{665} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{5})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{-75x} +25 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +25 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -360x+75x& = & 25+36 \\\Leftrightarrow & \color{red}{-285} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-285} & & \\\Leftrightarrow & x = \frac{-61}{285} & & \\ & V = \left\{ \frac{-61}{285} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{11})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{20}{11}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{60}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-60} & = & \color{red}{-165x} +77 \\\Leftrightarrow & -396x \color{red}{-60} \color{blue}{+60} \color{blue}{+165x} & = & \color{red}{-165x} +77 \color{blue}{+165x} \color{blue}{+60} \\\Leftrightarrow & -396x+165x& = & 77+60 \\\Leftrightarrow & \color{red}{-231} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-231} & & \\\Leftrightarrow & x = \frac{-137}{231} & & \\ & V = \left\{ \frac{-137}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1584}{ \color{blue}{132} }x+ \frac{360}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1584x \color{red}{+360} & = & \color{red}{660x} +55 \\\Leftrightarrow & -1584x \color{red}{+360} \color{blue}{-360} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{-360} \\\Leftrightarrow & -1584x-660x& = & 55-360 \\\Leftrightarrow & \color{red}{-2244} x& = & -305 \\\Leftrightarrow & x = \frac{-305}{-2244} & & \\\Leftrightarrow & x = \frac{305}{2244} & & \\ & V = \left\{ \frac{305}{2244} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -9x+\frac{12}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+12} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -99x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & -99x+55x& = & 6-12 \\\Leftrightarrow & \color{red}{-44} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-44} & & \\\Leftrightarrow & x = \frac{3}{22} & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)