Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 20x+\frac{16}{3}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+176} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 660x \color{red}{+176} \color{blue}{-176} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-176} \\\Leftrightarrow & 660x+99x& = & 6-176 \\\Leftrightarrow & \color{red}{759} x& = & -170 \\\Leftrightarrow & x = \frac{-170}{759} & & \\ & V = \left\{ \frac{-170}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & -9x+\frac{7}{9} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+24} & = & \color{red}{-81x} +7 \\\Leftrightarrow & -180x \color{red}{+24} \color{blue}{-24} \color{blue}{+81x} & = & \color{red}{-81x} +7 \color{blue}{+81x} \color{blue}{-24} \\\Leftrightarrow & -180x+81x& = & 7-24 \\\Leftrightarrow & \color{red}{-99} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-99} & & \\\Leftrightarrow & x = \frac{17}{99} & & \\ & V = \left\{ \frac{17}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{4}{3}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+4} & = & \color{red}{-27x} +10 \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{-4} \\\Leftrightarrow & -12x+27x& = & 10-4 \\\Leftrightarrow & \color{red}{15} x& = & 6 \\\Leftrightarrow & x = \frac{6}{15} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{9})& = & -6x+\frac{10}{3} \\\Leftrightarrow & 25x-\frac{10}{9}& = & -6x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{-10} & = & \color{red}{-54x} +30 \\\Leftrightarrow & 225x \color{red}{-10} \color{blue}{+10} \color{blue}{+54x} & = & \color{red}{-54x} +30 \color{blue}{+54x} \color{blue}{+10} \\\Leftrightarrow & 225x+54x& = & 30+10 \\\Leftrightarrow & \color{red}{279} x& = & 40 \\\Leftrightarrow & x = \frac{40}{279} & & \\ & V = \left\{ \frac{40}{279} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{-75x} +12 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{+75x} & = & \color{red}{-75x} +12 \color{blue}{+75x} \color{blue}{+70} \\\Leftrightarrow & -210x+75x& = & 12+70 \\\Leftrightarrow & \color{red}{-135} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-135} & & \\\Leftrightarrow & x = \frac{-82}{135} & & \\ & V = \left\{ \frac{-82}{135} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{3})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{28}{3}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-112} & = & \color{red}{24x} +9 \\\Leftrightarrow & 252x \color{red}{-112} \color{blue}{+112} \color{blue}{-24x} & = & \color{red}{24x} +9 \color{blue}{-24x} \color{blue}{+112} \\\Leftrightarrow & 252x-24x& = & 9+112 \\\Leftrightarrow & \color{red}{228} x& = & 121 \\\Leftrightarrow & x = \frac{121}{228} & & \\ & V = \left\{ \frac{121}{228} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+14} & = & \color{red}{-6x} +4 \\\Leftrightarrow & 63x \color{red}{+14} \color{blue}{-14} \color{blue}{+6x} & = & \color{red}{-6x} +4 \color{blue}{+6x} \color{blue}{-14} \\\Leftrightarrow & 63x+6x& = & 4-14 \\\Leftrightarrow & \color{red}{69} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{69} & & \\ & V = \left\{ \frac{-10}{69} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{-132x} +16 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{+132x} & = & \color{red}{-132x} +16 \color{blue}{+132x} \color{blue}{+165} \\\Leftrightarrow & -880x+132x& = & 16+165 \\\Leftrightarrow & \color{red}{-748} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-748} & & \\\Leftrightarrow & x = \frac{-181}{748} & & \\ & V = \left\{ \frac{-181}{748} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{9})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x-\frac{20}{9}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-100} & = & \color{red}{-315x} +18 \\\Leftrightarrow & -450x \color{red}{-100} \color{blue}{+100} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+100} \\\Leftrightarrow & -450x+315x& = & 18+100 \\\Leftrightarrow & \color{red}{-135} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-135} & & \\\Leftrightarrow & x = \frac{-118}{135} & & \\ & V = \left\{ \frac{-118}{135} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{2})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 9x-\frac{9}{2}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{198}{ \color{blue}{22} }x- \frac{99}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 198x \color{red}{-99} & = & \color{red}{-88x} +12 \\\Leftrightarrow & 198x \color{red}{-99} \color{blue}{+99} \color{blue}{+88x} & = & \color{red}{-88x} +12 \color{blue}{+88x} \color{blue}{+99} \\\Leftrightarrow & 198x+88x& = & 12+99 \\\Leftrightarrow & \color{red}{286} x& = & 111 \\\Leftrightarrow & x = \frac{111}{286} & & \\ & V = \left\{ \frac{111}{286} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-75x} +25 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +25 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 180x+75x& = & 25+36 \\\Leftrightarrow & \color{red}{255} x& = & 61 \\\Leftrightarrow & x = \frac{61}{255} & & \\ & V = \left\{ \frac{61}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{11})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -20x+\frac{16}{11}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{+16} & = & \color{red}{-99x} +2 \\\Leftrightarrow & -220x \color{red}{+16} \color{blue}{-16} \color{blue}{+99x} & = & \color{red}{-99x} +2 \color{blue}{+99x} \color{blue}{-16} \\\Leftrightarrow & -220x+99x& = & 2-16 \\\Leftrightarrow & \color{red}{-121} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-121} & & \\\Leftrightarrow & x = \frac{14}{121} & & \\ & V = \left\{ \frac{14}{121} \right\} & \\\end{align}\)