Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{8})& = & 6x+\frac{7}{5} \\\Leftrightarrow & -25x-\frac{15}{8}& = & 6x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1000}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{240}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1000x \color{red}{-75} & = & \color{red}{240x} +56 \\\Leftrightarrow & -1000x \color{red}{-75} \color{blue}{+75} \color{blue}{-240x} & = & \color{red}{240x} +56 \color{blue}{-240x} \color{blue}{+75} \\\Leftrightarrow & -1000x-240x& = & 56+75 \\\Leftrightarrow & \color{red}{-1240} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-1240} & & \\\Leftrightarrow & x = \frac{-131}{1240} & & \\ & V = \left\{ \frac{-131}{1240} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 14x-\frac{21}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-63} & = & \color{red}{99x} +88 \\\Leftrightarrow & 462x \color{red}{-63} \color{blue}{+63} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+63} \\\Leftrightarrow & 462x-99x& = & 88+63 \\\Leftrightarrow & \color{red}{363} x& = & 151 \\\Leftrightarrow & x = \frac{151}{363} & & \\ & V = \left\{ \frac{151}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{25}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+75} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 660x \color{red}{+75} \color{blue}{-75} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-75} \\\Leftrightarrow & 660x+231x& = & 44-75 \\\Leftrightarrow & \color{red}{891} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{891} & & \\ & V = \left\{ \frac{-31}{891} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{25}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{50}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+50} & = & \color{red}{-42x} +15 \\\Leftrightarrow & -60x \color{red}{+50} \color{blue}{-50} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{-50} \\\Leftrightarrow & -60x+42x& = & 15-50 \\\Leftrightarrow & \color{red}{-18} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-18} & & \\\Leftrightarrow & x = \frac{35}{18} & & \\ & V = \left\{ \frac{35}{18} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{-45x} +50 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{+45x} & = & \color{red}{-45x} +50 \color{blue}{+45x} \color{blue}{+54} \\\Leftrightarrow & -270x+45x& = & 50+54 \\\Leftrightarrow & \color{red}{-225} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-225} & & \\\Leftrightarrow & x = \frac{-104}{225} & & \\ & V = \left\{ \frac{-104}{225} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & -2x+\frac{9}{7} \\\Leftrightarrow & -28x-\frac{28}{3}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-196} & = & \color{red}{-42x} +27 \\\Leftrightarrow & -588x \color{red}{-196} \color{blue}{+196} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{+196} \\\Leftrightarrow & -588x+42x& = & 27+196 \\\Leftrightarrow & \color{red}{-546} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-546} & & \\\Leftrightarrow & x = \frac{-223}{546} & & \\ & V = \left\{ \frac{-223}{546} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{15}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{-15} & = & \color{red}{55x} +6 \\\Leftrightarrow & -99x \color{red}{-15} \color{blue}{+15} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+15} \\\Leftrightarrow & -99x-55x& = & 6+15 \\\Leftrightarrow & \color{red}{-154} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-154} & & \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{3})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{-63x} +12 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{-56} \\\Leftrightarrow & 84x+63x& = & 12-56 \\\Leftrightarrow & \color{red}{147} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{147} & & \\ & V = \left\{ \frac{-44}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 6x+\frac{7}{9} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 6x+\frac{7}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{432}{ \color{blue}{72} }x+ \frac{56}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{+189} & = & \color{red}{432x} +56 \\\Leftrightarrow & -2520x \color{red}{+189} \color{blue}{-189} \color{blue}{-432x} & = & \color{red}{432x} +56 \color{blue}{-432x} \color{blue}{-189} \\\Leftrightarrow & -2520x-432x& = & 56-189 \\\Leftrightarrow & \color{red}{-2952} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-2952} & & \\\Leftrightarrow & x = \frac{133}{2952} & & \\ & V = \left\{ \frac{133}{2952} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{-75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & 400x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & 400x+140x& = & 24+75 \\\Leftrightarrow & \color{red}{540} x& = & 99 \\\Leftrightarrow & x = \frac{99}{540} & & \\\Leftrightarrow & x = \frac{11}{60} & & \\ & V = \left\{ \frac{11}{60} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{30x} +25 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-30x} & = & \color{red}{30x} +25 \color{blue}{-30x} \color{blue}{+12} \\\Leftrightarrow & -80x-30x& = & 25+12 \\\Leftrightarrow & \color{red}{-110} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-110} & & \\\Leftrightarrow & x = \frac{-37}{110} & & \\ & V = \left\{ \frac{-37}{110} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{6})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{25}{6}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-25} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -60x \color{red}{-25} \color{blue}{+25} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{+25} \\\Leftrightarrow & -60x+42x& = & 5+25 \\\Leftrightarrow & \color{red}{-18} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-18} & & \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)