Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{3})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -6x-\frac{4}{3}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{-147x} +18 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{+147x} & = & \color{red}{-147x} +18 \color{blue}{+147x} \color{blue}{+28} \\\Leftrightarrow & -126x+147x& = & 18+28 \\\Leftrightarrow & \color{red}{21} x& = & 46 \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{10})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{+27} & = & \color{red}{210x} +100 \\\Leftrightarrow & 270x \color{red}{+27} \color{blue}{-27} \color{blue}{-210x} & = & \color{red}{210x} +100 \color{blue}{-210x} \color{blue}{-27} \\\Leftrightarrow & 270x-210x& = & 100-27 \\\Leftrightarrow & \color{red}{60} x& = & 73 \\\Leftrightarrow & x = \frac{73}{60} & & \\ & V = \left\{ \frac{73}{60} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{4}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+44} & = & \color{red}{-539x} +56 \\\Leftrightarrow & -462x \color{red}{+44} \color{blue}{-44} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{-44} \\\Leftrightarrow & -462x+539x& = & 56-44 \\\Leftrightarrow & \color{red}{77} x& = & 12 \\\Leftrightarrow & x = \frac{12}{77} & & \\ & V = \left\{ \frac{12}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{25x} +8 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & 90x-25x& = & 8+18 \\\Leftrightarrow & \color{red}{65} x& = & 26 \\\Leftrightarrow & x = \frac{26}{65} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & -3x+\frac{6}{7} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-10} & = & \color{red}{-21x} +6 \\\Leftrightarrow & -175x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +6 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & -175x+21x& = & 6+10 \\\Leftrightarrow & \color{red}{-154} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-154} & & \\\Leftrightarrow & x = \frac{-8}{77} & & \\ & V = \left\{ \frac{-8}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+8} & = & \color{red}{63x} +6 \\\Leftrightarrow & -90x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & -90x-63x& = & 6-8 \\\Leftrightarrow & \color{red}{-153} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-153} & & \\\Leftrightarrow & x = \frac{2}{153} & & \\ & V = \left\{ \frac{2}{153} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{165x} +22 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & 594x-165x& = & 22+54 \\\Leftrightarrow & \color{red}{429} x& = & 76 \\\Leftrightarrow & x = \frac{76}{429} & & \\ & V = \left\{ \frac{76}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{25}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{175}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+175} & = & \color{red}{-147x} +30 \\\Leftrightarrow & -210x \color{red}{+175} \color{blue}{-175} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{-175} \\\Leftrightarrow & -210x+147x& = & 30-175 \\\Leftrightarrow & \color{red}{-63} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-63} & & \\\Leftrightarrow & x = \frac{145}{63} & & \\ & V = \left\{ \frac{145}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{12})& = & -4x+\frac{7}{5} \\\Leftrightarrow & 25x-\frac{25}{12}& = & -4x+\frac{7}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1500}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{-240}{ \color{blue}{60} }x+ \frac{84}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1500x \color{red}{-125} & = & \color{red}{-240x} +84 \\\Leftrightarrow & 1500x \color{red}{-125} \color{blue}{+125} \color{blue}{+240x} & = & \color{red}{-240x} +84 \color{blue}{+240x} \color{blue}{+125} \\\Leftrightarrow & 1500x+240x& = & 84+125 \\\Leftrightarrow & \color{red}{1740} x& = & 209 \\\Leftrightarrow & x = \frac{209}{1740} & & \\ & V = \left\{ \frac{209}{1740} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +40 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 40+84 \\\Leftrightarrow & \color{red}{-245} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-245} & & \\\Leftrightarrow & x = \frac{-124}{245} & & \\ & V = \left\{ \frac{-124}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{6})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -14x+\frac{35}{6}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{90x} +27 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-175} \\\Leftrightarrow & -420x-90x& = & 27-175 \\\Leftrightarrow & \color{red}{-510} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-510} & & \\\Leftrightarrow & x = \frac{74}{255} & & \\ & V = \left\{ \frac{74}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{12})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -14x-\frac{35}{12}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-840}{ \color{blue}{60} }x- \frac{175}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{300x} +72 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{-300x} & = & \color{red}{300x} +72 \color{blue}{-300x} \color{blue}{+175} \\\Leftrightarrow & -840x-300x& = & 72+175 \\\Leftrightarrow & \color{red}{-1140} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-1140} & & \\\Leftrightarrow & x = \frac{-13}{60} & & \\ & V = \left\{ \frac{-13}{60} \right\} & \\\end{align}\)