Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -350x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{-105} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-105} & & \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{+18} & = & \color{red}{99x} +6 \\\Leftrightarrow & -198x \color{red}{+18} \color{blue}{-18} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{-18} \\\Leftrightarrow & -198x-99x& = & 6-18 \\\Leftrightarrow & \color{red}{-297} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-297} & & \\\Leftrightarrow & x = \frac{4}{99} & & \\ & V = \left\{ \frac{4}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{7})& = & -8x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+165} & = & \color{red}{-616x} +56 \\\Leftrightarrow & 1155x \color{red}{+165} \color{blue}{-165} \color{blue}{+616x} & = & \color{red}{-616x} +56 \color{blue}{+616x} \color{blue}{-165} \\\Leftrightarrow & 1155x+616x& = & 56-165 \\\Leftrightarrow & \color{red}{1771} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1771} & & \\ & V = \left\{ \frac{-109}{1771} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+30} & = & \color{red}{-55x} +4 \\\Leftrightarrow & -132x \color{red}{+30} \color{blue}{-30} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{-30} \\\Leftrightarrow & -132x+55x& = & 4-30 \\\Leftrightarrow & \color{red}{-77} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-77} & & \\\Leftrightarrow & x = \frac{26}{77} & & \\ & V = \left\{ \frac{26}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-66} & = & \color{red}{-385x} +35 \\\Leftrightarrow & 616x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 616x+385x& = & 35+66 \\\Leftrightarrow & \color{red}{1001} x& = & 101 \\\Leftrightarrow & x = \frac{101}{1001} & & \\ & V = \left\{ \frac{101}{1001} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{7})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 18x+\frac{24}{7}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{48}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+48} & = & \color{red}{-70x} +49 \\\Leftrightarrow & 252x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 252x+70x& = & 49-48 \\\Leftrightarrow & \color{red}{322} x& = & 1 \\\Leftrightarrow & x = \frac{1}{322} & & \\ & V = \left\{ \frac{1}{322} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -3x+\frac{5}{8} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -3x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{+64} & = & \color{red}{-72x} +15 \\\Leftrightarrow & 192x \color{red}{+64} \color{blue}{-64} \color{blue}{+72x} & = & \color{red}{-72x} +15 \color{blue}{+72x} \color{blue}{-64} \\\Leftrightarrow & 192x+72x& = & 15-64 \\\Leftrightarrow & \color{red}{264} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{264} & & \\ & V = \left\{ \frac{-49}{264} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 20x-\frac{16}{7}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1680x \color{red}{-192} & = & \color{red}{-252x} +35 \\\Leftrightarrow & 1680x \color{red}{-192} \color{blue}{+192} \color{blue}{+252x} & = & \color{red}{-252x} +35 \color{blue}{+252x} \color{blue}{+192} \\\Leftrightarrow & 1680x+252x& = & 35+192 \\\Leftrightarrow & \color{red}{1932} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1932} & & \\ & V = \left\{ \frac{227}{1932} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-48} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -420x \color{red}{-48} \color{blue}{+48} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{+48} \\\Leftrightarrow & -420x+63x& = & 56+48 \\\Leftrightarrow & \color{red}{-357} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-357} & & \\\Leftrightarrow & x = \frac{-104}{357} & & \\ & V = \left\{ \frac{-104}{357} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -240x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{-345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-345} & & \\\Leftrightarrow & x = \frac{26}{345} & & \\ & V = \left\{ \frac{26}{345} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-154} & = & \color{red}{-99x} +12 \\\Leftrightarrow & -462x \color{red}{-154} \color{blue}{+154} \color{blue}{+99x} & = & \color{red}{-99x} +12 \color{blue}{+99x} \color{blue}{+154} \\\Leftrightarrow & -462x+99x& = & 12+154 \\\Leftrightarrow & \color{red}{-363} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-363} & & \\\Leftrightarrow & x = \frac{-166}{363} & & \\ & V = \left\{ \frac{-166}{363} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{2})& = & -2x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{15}{2}& = & -2x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+165} & = & \color{red}{-44x} +8 \\\Leftrightarrow & 330x \color{red}{+165} \color{blue}{-165} \color{blue}{+44x} & = & \color{red}{-44x} +8 \color{blue}{+44x} \color{blue}{-165} \\\Leftrightarrow & 330x+44x& = & 8-165 \\\Leftrightarrow & \color{red}{374} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{374} & & \\ & V = \left\{ \frac{-157}{374} \right\} & \\\end{align}\)