Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x+\frac{6}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+42} & = & \color{red}{385x} +44 \\\Leftrightarrow & -924x \color{red}{+42} \color{blue}{-42} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-42} \\\Leftrightarrow & -924x-385x& = & 44-42 \\\Leftrightarrow & \color{red}{-1309} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-1309} & & \\\Leftrightarrow & x = \frac{-2}{1309} & & \\ & V = \left\{ \frac{-2}{1309} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{+10} \\\Leftrightarrow & -28x+35x& = & 9+10 \\\Leftrightarrow & \color{red}{7} x& = & 19 \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+12} & = & \color{red}{-55x} +2 \\\Leftrightarrow & 132x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & 132x+55x& = & 2-12 \\\Leftrightarrow & \color{red}{187} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{187} & & \\ & V = \left\{ \frac{-10}{187} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & 3x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{8}{3}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-88} & = & \color{red}{99x} +30 \\\Leftrightarrow & -660x \color{red}{-88} \color{blue}{+88} \color{blue}{-99x} & = & \color{red}{99x} +30 \color{blue}{-99x} \color{blue}{+88} \\\Leftrightarrow & -660x-99x& = & 30+88 \\\Leftrightarrow & \color{red}{-759} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-759} & & \\\Leftrightarrow & x = \frac{-118}{759} & & \\ & V = \left\{ \frac{-118}{759} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{9})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 8x+\frac{4}{9}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{576}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 576x \color{red}{+32} & = & \color{red}{504x} +63 \\\Leftrightarrow & 576x \color{red}{+32} \color{blue}{-32} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{-32} \\\Leftrightarrow & 576x-504x& = & 63-32 \\\Leftrightarrow & \color{red}{72} x& = & 31 \\\Leftrightarrow & x = \frac{31}{72} & & \\ & V = \left\{ \frac{31}{72} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{2})& = & -4x+\frac{8}{9} \\\Leftrightarrow & -15x-\frac{25}{2}& = & -4x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{-72}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{-225} & = & \color{red}{-72x} +16 \\\Leftrightarrow & -270x \color{red}{-225} \color{blue}{+225} \color{blue}{+72x} & = & \color{red}{-72x} +16 \color{blue}{+72x} \color{blue}{+225} \\\Leftrightarrow & -270x+72x& = & 16+225 \\\Leftrightarrow & \color{red}{-198} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-198} & & \\\Leftrightarrow & x = \frac{-241}{198} & & \\ & V = \left\{ \frac{-241}{198} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{8})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{15}{8}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{144}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 144x \color{red}{-45} & = & \color{red}{-120x} +80 \\\Leftrightarrow & 144x \color{red}{-45} \color{blue}{+45} \color{blue}{+120x} & = & \color{red}{-120x} +80 \color{blue}{+120x} \color{blue}{+45} \\\Leftrightarrow & 144x+120x& = & 80+45 \\\Leftrightarrow & \color{red}{264} x& = & 125 \\\Leftrightarrow & x = \frac{125}{264} & & \\ & V = \left\{ \frac{125}{264} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{4})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{9}{4}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{+9} & = & \color{red}{28x} +6 \\\Leftrightarrow & -24x \color{red}{+9} \color{blue}{-9} \color{blue}{-28x} & = & \color{red}{28x} +6 \color{blue}{-28x} \color{blue}{-9} \\\Leftrightarrow & -24x-28x& = & 6-9 \\\Leftrightarrow & \color{red}{-52} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-52} & & \\\Leftrightarrow & x = \frac{3}{52} & & \\ & V = \left\{ \frac{3}{52} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -14x+4& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{20}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+20} & = & \color{red}{15x} +6 \\\Leftrightarrow & -70x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +6 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & -70x-15x& = & 6-20 \\\Leftrightarrow & \color{red}{-85} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-85} & & \\\Leftrightarrow & x = \frac{14}{85} & & \\ & V = \left\{ \frac{14}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-720}{ \color{blue}{30} }x- \frac{144}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -720x \color{red}{-144} & = & \color{red}{210x} +25 \\\Leftrightarrow & -720x \color{red}{-144} \color{blue}{+144} \color{blue}{-210x} & = & \color{red}{210x} +25 \color{blue}{-210x} \color{blue}{+144} \\\Leftrightarrow & -720x-210x& = & 25+144 \\\Leftrightarrow & \color{red}{-930} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-930} & & \\\Leftrightarrow & x = \frac{-169}{930} & & \\ & V = \left\{ \frac{-169}{930} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{45x} +50 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +50 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 60x-45x& = & 50-12 \\\Leftrightarrow & \color{red}{15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{15} & & \\ & V = \left\{ \frac{38}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{140x} +16 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & -120x-140x& = & 16+75 \\\Leftrightarrow & \color{red}{-260} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-260} & & \\\Leftrightarrow & x = \frac{-7}{20} & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)