Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-54} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -504x \color{red}{-54} \color{blue}{+54} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+54} \\\Leftrightarrow & -504x+189x& = & 28+54 \\\Leftrightarrow & \color{red}{-315} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-315} & & \\\Leftrightarrow & x = \frac{-82}{315} & & \\ & V = \left\{ \frac{-82}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{-45x} +40 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{+45x} & = & \color{red}{-45x} +40 \color{blue}{+45x} \color{blue}{-36} \\\Leftrightarrow & 300x+45x& = & 40-36 \\\Leftrightarrow & \color{red}{345} x& = & 4 \\\Leftrightarrow & x = \frac{4}{345} & & \\ & V = \left\{ \frac{4}{345} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-75} & = & \color{red}{-140x} +14 \\\Leftrightarrow & -500x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +14 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -500x+140x& = & 14+75 \\\Leftrightarrow & \color{red}{-360} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-360} & & \\\Leftrightarrow & x = \frac{-89}{360} & & \\ & V = \left\{ \frac{-89}{360} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{3})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-24} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -54x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & -54x+63x& = & 8+24 \\\Leftrightarrow & \color{red}{9} x& = & 32 \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{7})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{8}{7}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+8} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -56x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & -56x+21x& = & 8-8 \\\Leftrightarrow & \color{red}{-35} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-35} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{9})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 20x+\frac{16}{9}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{112}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+112} & = & \color{red}{-189x} +54 \\\Leftrightarrow & 1260x \color{red}{+112} \color{blue}{-112} \color{blue}{+189x} & = & \color{red}{-189x} +54 \color{blue}{+189x} \color{blue}{-112} \\\Leftrightarrow & 1260x+189x& = & 54-112 \\\Leftrightarrow & \color{red}{1449} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1449} & & \\ & V = \left\{ \frac{-58}{1449} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{3})& = & 4x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{35}{3}& = & 4x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-245} & = & \color{red}{84x} +18 \\\Leftrightarrow & 441x \color{red}{-245} \color{blue}{+245} \color{blue}{-84x} & = & \color{red}{84x} +18 \color{blue}{-84x} \color{blue}{+245} \\\Leftrightarrow & 441x-84x& = & 18+245 \\\Leftrightarrow & \color{red}{357} x& = & 263 \\\Leftrightarrow & x = \frac{263}{357} & & \\ & V = \left\{ \frac{263}{357} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1800}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1800x \color{red}{+144} & = & \color{red}{420x} +35 \\\Leftrightarrow & -1800x \color{red}{+144} \color{blue}{-144} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{-144} \\\Leftrightarrow & -1800x-420x& = & 35-144 \\\Leftrightarrow & \color{red}{-2220} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-2220} & & \\\Leftrightarrow & x = \frac{109}{2220} & & \\ & V = \left\{ \frac{109}{2220} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & 4x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{9}{5}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+18} & = & \color{red}{40x} +9 \\\Leftrightarrow & 150x \color{red}{+18} \color{blue}{-18} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{-18} \\\Leftrightarrow & 150x-40x& = & 9-18 \\\Leftrightarrow & \color{red}{110} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{110} & & \\ & V = \left\{ \frac{-9}{110} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -1350x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{-1035} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-1035} & & \\\Leftrightarrow & x = \frac{58}{1035} & & \\ & V = \left\{ \frac{58}{1035} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{7})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{9}{7}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+99} & = & \color{red}{-154x} +56 \\\Leftrightarrow & 1155x \color{red}{+99} \color{blue}{-99} \color{blue}{+154x} & = & \color{red}{-154x} +56 \color{blue}{+154x} \color{blue}{-99} \\\Leftrightarrow & 1155x+154x& = & 56-99 \\\Leftrightarrow & \color{red}{1309} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{1309} & & \\ & V = \left\{ \frac{-43}{1309} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+10} & = & \color{red}{-33x} +10 \\\Leftrightarrow & 220x \color{red}{+10} \color{blue}{-10} \color{blue}{+33x} & = & \color{red}{-33x} +10 \color{blue}{+33x} \color{blue}{-10} \\\Leftrightarrow & 220x+33x& = & 10-10 \\\Leftrightarrow & \color{red}{253} x& = & 0 \\\Leftrightarrow & x = \frac{0}{253} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)