Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{9})& = & 6x+\frac{8}{7} \\\Leftrightarrow & 25x-\frac{25}{9}& = & 6x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{378}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-175} & = & \color{red}{378x} +72 \\\Leftrightarrow & 1575x \color{red}{-175} \color{blue}{+175} \color{blue}{-378x} & = & \color{red}{378x} +72 \color{blue}{-378x} \color{blue}{+175} \\\Leftrightarrow & 1575x-378x& = & 72+175 \\\Leftrightarrow & \color{red}{1197} x& = & 247 \\\Leftrightarrow & x = \frac{247}{1197} & & \\\Leftrightarrow & x = \frac{13}{63} & & \\ & V = \left\{ \frac{13}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{63x} +4 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+4} \\\Leftrightarrow & 54x-63x& = & 4+4 \\\Leftrightarrow & \color{red}{-9} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-9} & & \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{8})& = & 8x+\frac{2}{11} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-231} & = & \color{red}{704x} +16 \\\Leftrightarrow & -1848x \color{red}{-231} \color{blue}{+231} \color{blue}{-704x} & = & \color{red}{704x} +16 \color{blue}{-704x} \color{blue}{+231} \\\Leftrightarrow & -1848x-704x& = & 16+231 \\\Leftrightarrow & \color{red}{-2552} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-2552} & & \\\Leftrightarrow & x = \frac{-247}{2552} & & \\ & V = \left\{ \frac{-247}{2552} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-50} & = & \color{red}{220x} +66 \\\Leftrightarrow & -825x \color{red}{-50} \color{blue}{+50} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{+50} \\\Leftrightarrow & -825x-220x& = & 66+50 \\\Leftrightarrow & \color{red}{-1045} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-1045} & & \\\Leftrightarrow & x = \frac{-116}{1045} & & \\ & V = \left\{ \frac{-116}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{12}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-12} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -220x \color{red}{-12} \color{blue}{+12} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+12} \\\Leftrightarrow & -220x+99x& = & 6+12 \\\Leftrightarrow & \color{red}{-121} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-121} & & \\\Leftrightarrow & x = \frac{-18}{121} & & \\ & V = \left\{ \frac{-18}{121} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{11})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{35}{11}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+105} & = & \color{red}{-264x} +22 \\\Leftrightarrow & -693x \color{red}{+105} \color{blue}{-105} \color{blue}{+264x} & = & \color{red}{-264x} +22 \color{blue}{+264x} \color{blue}{-105} \\\Leftrightarrow & -693x+264x& = & 22-105 \\\Leftrightarrow & \color{red}{-429} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-429} & & \\\Leftrightarrow & x = \frac{83}{429} & & \\ & V = \left\{ \frac{83}{429} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{12}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+12} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 88x \color{red}{+12} \color{blue}{-12} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-12} \\\Leftrightarrow & 88x+99x& = & 6-12 \\\Leftrightarrow & \color{red}{187} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{187} & & \\ & V = \left\{ \frac{-6}{187} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{+40} & = & \color{red}{315x} +54 \\\Leftrightarrow & 450x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & 450x-315x& = & 54-40 \\\Leftrightarrow & \color{red}{135} x& = & 14 \\\Leftrightarrow & x = \frac{14}{135} & & \\ & V = \left\{ \frac{14}{135} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-112} & = & \color{red}{231x} +110 \\\Leftrightarrow & 1540x \color{red}{-112} \color{blue}{+112} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+112} \\\Leftrightarrow & 1540x-231x& = & 110+112 \\\Leftrightarrow & \color{red}{1309} x& = & 222 \\\Leftrightarrow & x = \frac{222}{1309} & & \\ & V = \left\{ \frac{222}{1309} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -4x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{-28x} +4 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-6} \\\Leftrightarrow & 63x+28x& = & 4-6 \\\Leftrightarrow & \color{red}{91} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{91} & & \\ & V = \left\{ \frac{-2}{91} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{24}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & -792x+165x& = & 110-72 \\\Leftrightarrow & \color{red}{-627} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-627} & & \\\Leftrightarrow & x = \frac{-2}{33} & & \\ & V = \left\{ \frac{-2}{33} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 6x-\frac{4}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-20} & = & \color{red}{75x} +6 \\\Leftrightarrow & 90x \color{red}{-20} \color{blue}{+20} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{+20} \\\Leftrightarrow & 90x-75x& = & 6+20 \\\Leftrightarrow & \color{red}{15} x& = & 26 \\\Leftrightarrow & x = \frac{26}{15} & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)