Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{18}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+54} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{+54} \color{blue}{-54} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-54} \\\Leftrightarrow & 270x+75x& = & 50-54 \\\Leftrightarrow & \color{red}{345} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{345} & & \\ & V = \left\{ \frac{-4}{345} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-12} & = & \color{red}{35x} +2 \\\Leftrightarrow & 45x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 45x-35x& = & 2+12 \\\Leftrightarrow & \color{red}{10} x& = & 14 \\\Leftrightarrow & x = \frac{14}{10} & & \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & 4x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{224x} +80 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{-224x} & = & \color{red}{224x} +80 \color{blue}{-224x} \color{blue}{+105} \\\Leftrightarrow & 840x-224x& = & 80+105 \\\Leftrightarrow & \color{red}{616} x& = & 185 \\\Leftrightarrow & x = \frac{185}{616} & & \\ & V = \left\{ \frac{185}{616} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{4}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+4} & = & \color{red}{-63x} +24 \\\Leftrightarrow & 72x \color{red}{+4} \color{blue}{-4} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-4} \\\Leftrightarrow & 72x+63x& = & 24-4 \\\Leftrightarrow & \color{red}{135} x& = & 20 \\\Leftrightarrow & x = \frac{20}{135} & & \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{10}{7}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{-40} & = & \color{red}{-252x} +63 \\\Leftrightarrow & 560x \color{red}{-40} \color{blue}{+40} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{+40} \\\Leftrightarrow & 560x+252x& = & 63+40 \\\Leftrightarrow & \color{red}{812} x& = & 103 \\\Leftrightarrow & x = \frac{103}{812} & & \\ & V = \left\{ \frac{103}{812} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{176}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 176x \color{red}{-40} & = & \color{red}{220x} +33 \\\Leftrightarrow & 176x \color{red}{-40} \color{blue}{+40} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+40} \\\Leftrightarrow & 176x-220x& = & 33+40 \\\Leftrightarrow & \color{red}{-44} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-44} & & \\\Leftrightarrow & x = \frac{-73}{44} & & \\ & V = \left\{ \frac{-73}{44} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 6x+\frac{7}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 6x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{18}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{18x} +7 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{-18x} & = & \color{red}{18x} +7 \color{blue}{-18x} \color{blue}{+14} \\\Leftrightarrow & -105x-18x& = & 7+14 \\\Leftrightarrow & \color{red}{-123} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-123} & & \\\Leftrightarrow & x = \frac{-7}{41} & & \\ & V = \left\{ \frac{-7}{41} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+1)& = & 8x+\frac{4}{9} \\\Leftrightarrow & -21x-7& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{63}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-63} & = & \color{red}{72x} +4 \\\Leftrightarrow & -189x \color{red}{-63} \color{blue}{+63} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{+63} \\\Leftrightarrow & -189x-72x& = & 4+63 \\\Leftrightarrow & \color{red}{-261} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-261} & & \\\Leftrightarrow & x = \frac{-67}{261} & & \\ & V = \left\{ \frac{-67}{261} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{9})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 35x+\frac{14}{9}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2520}{ \color{blue}{72} }x+ \frac{112}{ \color{blue}{72} })& = & (\frac{-144}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2520x \color{red}{+112} & = & \color{red}{-144x} +63 \\\Leftrightarrow & 2520x \color{red}{+112} \color{blue}{-112} \color{blue}{+144x} & = & \color{red}{-144x} +63 \color{blue}{+144x} \color{blue}{-112} \\\Leftrightarrow & 2520x+144x& = & 63-112 \\\Leftrightarrow & \color{red}{2664} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{2664} & & \\ & V = \left\{ \frac{-49}{2664} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{25}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{150}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{294x} +35 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{+150} \\\Leftrightarrow & -840x-294x& = & 35+150 \\\Leftrightarrow & \color{red}{-1134} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-1134} & & \\\Leftrightarrow & x = \frac{-185}{1134} & & \\ & V = \left\{ \frac{-185}{1134} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+80} & = & \color{red}{495x} +66 \\\Leftrightarrow & 440x \color{red}{+80} \color{blue}{-80} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{-80} \\\Leftrightarrow & 440x-495x& = & 66-80 \\\Leftrightarrow & \color{red}{-55} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-55} & & \\\Leftrightarrow & x = \frac{14}{55} & & \\ & V = \left\{ \frac{14}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{147x} +30 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{+56} \\\Leftrightarrow & -210x-147x& = & 30+56 \\\Leftrightarrow & \color{red}{-357} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-357} & & \\\Leftrightarrow & x = \frac{-86}{357} & & \\ & V = \left\{ \frac{-86}{357} \right\} & \\\end{align}\)