Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+8} & = & \color{red}{77x} +4 \\\Leftrightarrow & 220x \color{red}{+8} \color{blue}{-8} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-8} \\\Leftrightarrow & 220x-77x& = & 4-8 \\\Leftrightarrow & \color{red}{143} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{143} & & \\ & V = \left\{ \frac{-4}{143} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{9})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{225x} +54 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{-225x} & = & \color{red}{225x} +54 \color{blue}{-225x} \color{blue}{+40} \\\Leftrightarrow & 360x-225x& = & 54+40 \\\Leftrightarrow & \color{red}{135} x& = & 94 \\\Leftrightarrow & x = \frac{94}{135} & & \\ & V = \left\{ \frac{94}{135} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{900}{ \color{blue}{90} }x- \frac{40}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 900x \color{red}{-40} & = & \color{red}{810x} +27 \\\Leftrightarrow & 900x \color{red}{-40} \color{blue}{+40} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{+40} \\\Leftrightarrow & 900x-810x& = & 27+40 \\\Leftrightarrow & \color{red}{90} x& = & 67 \\\Leftrightarrow & x = \frac{67}{90} & & \\ & V = \left\{ \frac{67}{90} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{11})& = & -9x+\frac{7}{12} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -9x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1056}{ \color{blue}{132} }x- \frac{96}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1056x \color{red}{-96} & = & \color{red}{-1188x} +77 \\\Leftrightarrow & 1056x \color{red}{-96} \color{blue}{+96} \color{blue}{+1188x} & = & \color{red}{-1188x} +77 \color{blue}{+1188x} \color{blue}{+96} \\\Leftrightarrow & 1056x+1188x& = & 77+96 \\\Leftrightarrow & \color{red}{2244} x& = & 173 \\\Leftrightarrow & x = \frac{173}{2244} & & \\ & V = \left\{ \frac{173}{2244} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{9}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+81} & = & \color{red}{225x} +40 \\\Leftrightarrow & 270x \color{red}{+81} \color{blue}{-81} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{-81} \\\Leftrightarrow & 270x-225x& = & 40-81 \\\Leftrightarrow & \color{red}{45} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{45} & & \\ & V = \left\{ \frac{-41}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -360x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{-435} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-435} & & \\\Leftrightarrow & x = \frac{-4}{435} & & \\ & V = \left\{ \frac{-4}{435} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{-40} & = & \color{red}{18x} +9 \\\Leftrightarrow & 48x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & 48x-18x& = & 9+40 \\\Leftrightarrow & \color{red}{30} x& = & 49 \\\Leftrightarrow & x = \frac{49}{30} & & \\ & V = \left\{ \frac{49}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -120x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{-95} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-95} & & \\\Leftrightarrow & x = \frac{6}{95} & & \\ & V = \left\{ \frac{6}{95} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{-231x} +56 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +56 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & 1540x+231x& = & 56-220 \\\Leftrightarrow & \color{red}{1771} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{1771} & & \\ & V = \left\{ \frac{-164}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{275x} +15 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{-99} \\\Leftrightarrow & -660x-275x& = & 15-99 \\\Leftrightarrow & \color{red}{-935} x& = & -84 \\\Leftrightarrow & x = \frac{-84}{-935} & & \\\Leftrightarrow & x = \frac{84}{935} & & \\ & V = \left\{ \frac{84}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+16} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 176x \color{red}{+16} \color{blue}{-16} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{-16} \\\Leftrightarrow & 176x+110x& = & 99-16 \\\Leftrightarrow & \color{red}{286} x& = & 83 \\\Leftrightarrow & x = \frac{83}{286} & & \\ & V = \left\{ \frac{83}{286} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{+216} & = & \color{red}{315x} +20 \\\Leftrightarrow & 1350x \color{red}{+216} \color{blue}{-216} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-216} \\\Leftrightarrow & 1350x-315x& = & 20-216 \\\Leftrightarrow & \color{red}{1035} x& = & -196 \\\Leftrightarrow & x = \frac{-196}{1035} & & \\ & V = \left\{ \frac{-196}{1035} \right\} & \\\end{align}\)