Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-30} & = & \color{red}{-245x} +21 \\\Leftrightarrow & -350x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & -350x+245x& = & 21+30 \\\Leftrightarrow & \color{red}{-105} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-105} & & \\\Leftrightarrow & x = \frac{-17}{35} & & \\ & V = \left\{ \frac{-17}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{176x} +77 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{-176x} & = & \color{red}{176x} +77 \color{blue}{-176x} \color{blue}{+30} \\\Leftrightarrow & -330x-176x& = & 77+30 \\\Leftrightarrow & \color{red}{-506} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-506} & & \\\Leftrightarrow & x = \frac{-107}{506} & & \\ & V = \left\{ \frac{-107}{506} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-50x} +9 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+12} \\\Leftrightarrow & 60x+50x& = & 9+12 \\\Leftrightarrow & \color{red}{110} x& = & 21 \\\Leftrightarrow & x = \frac{21}{110} & & \\ & V = \left\{ \frac{21}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{12}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+12} & = & \color{red}{-55x} +5 \\\Leftrightarrow & -264x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & -264x+55x& = & 5-12 \\\Leftrightarrow & \color{red}{-209} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-209} & & \\\Leftrightarrow & x = \frac{7}{209} & & \\ & V = \left\{ \frac{7}{209} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+24} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -264x \color{red}{+24} \color{blue}{-24} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{-24} \\\Leftrightarrow & -264x+99x& = & 44-24 \\\Leftrightarrow & \color{red}{-165} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-165} & & \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+24} & = & \color{red}{-147x} +28 \\\Leftrightarrow & 252x \color{red}{+24} \color{blue}{-24} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-24} \\\Leftrightarrow & 252x+147x& = & 28-24 \\\Leftrightarrow & \color{red}{399} x& = & 4 \\\Leftrightarrow & x = \frac{4}{399} & & \\ & V = \left\{ \frac{4}{399} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 4x+\frac{4}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{-20} \\\Leftrightarrow & 140x+105x& = & 42-20 \\\Leftrightarrow & \color{red}{245} x& = & 22 \\\Leftrightarrow & x = \frac{22}{245} & & \\ & V = \left\{ \frac{22}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{-245x} +20 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 1050x+245x& = & 20-84 \\\Leftrightarrow & \color{red}{1295} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{1295} & & \\ & V = \left\{ \frac{-64}{1295} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{20}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+20} & = & \color{red}{-44x} +6 \\\Leftrightarrow & -165x \color{red}{+20} \color{blue}{-20} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{-20} \\\Leftrightarrow & -165x+44x& = & 6-20 \\\Leftrightarrow & \color{red}{-121} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-121} & & \\\Leftrightarrow & x = \frac{14}{121} & & \\ & V = \left\{ \frac{14}{121} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{-63x} +5 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +5 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 180x+63x& = & 5-8 \\\Leftrightarrow & \color{red}{243} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{243} & & \\\Leftrightarrow & x = \frac{-1}{81} & & \\ & V = \left\{ \frac{-1}{81} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{16}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+48} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -660x \color{red}{+48} \color{blue}{-48} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{-48} \\\Leftrightarrow & -660x+99x& = & 44-48 \\\Leftrightarrow & \color{red}{-561} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-561} & & \\\Leftrightarrow & x = \frac{4}{561} & & \\ & V = \left\{ \frac{4}{561} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{5}{4} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+24} & = & \color{red}{-112x} +35 \\\Leftrightarrow & -420x \color{red}{+24} \color{blue}{-24} \color{blue}{+112x} & = & \color{red}{-112x} +35 \color{blue}{+112x} \color{blue}{-24} \\\Leftrightarrow & -420x+112x& = & 35-24 \\\Leftrightarrow & \color{red}{-308} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-308} & & \\\Leftrightarrow & x = \frac{-1}{28} & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)