Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -20x+\frac{25}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{275}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+275} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -1540x \color{red}{+275} \color{blue}{-275} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-275} \\\Leftrightarrow & -1540x+539x& = & 28-275 \\\Leftrightarrow & \color{red}{-1001} x& = & -247 \\\Leftrightarrow & x = \frac{-247}{-1001} & & \\\Leftrightarrow & x = \frac{19}{77} & & \\ & V = \left\{ \frac{19}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{8}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+8} & = & \color{red}{77x} +4 \\\Leftrightarrow & 110x \color{red}{+8} \color{blue}{-8} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-8} \\\Leftrightarrow & 110x-77x& = & 4-8 \\\Leftrightarrow & \color{red}{33} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{-12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 80x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 80x+25x& = & 4+12 \\\Leftrightarrow & \color{red}{105} x& = & 16 \\\Leftrightarrow & x = \frac{16}{105} & & \\ & V = \left\{ \frac{16}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{3})& = & 9x+\frac{8}{11} \\\Leftrightarrow & 28x-\frac{28}{3}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-308} & = & \color{red}{297x} +24 \\\Leftrightarrow & 924x \color{red}{-308} \color{blue}{+308} \color{blue}{-297x} & = & \color{red}{297x} +24 \color{blue}{-297x} \color{blue}{+308} \\\Leftrightarrow & 924x-297x& = & 24+308 \\\Leftrightarrow & \color{red}{627} x& = & 332 \\\Leftrightarrow & x = \frac{332}{627} & & \\ & V = \left\{ \frac{332}{627} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{7})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{15}{7}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+30} & = & \color{red}{-28x} +63 \\\Leftrightarrow & 350x \color{red}{+30} \color{blue}{-30} \color{blue}{+28x} & = & \color{red}{-28x} +63 \color{blue}{+28x} \color{blue}{-30} \\\Leftrightarrow & 350x+28x& = & 63-30 \\\Leftrightarrow & \color{red}{378} x& = & 33 \\\Leftrightarrow & x = \frac{33}{378} & & \\\Leftrightarrow & x = \frac{11}{126} & & \\ & V = \left\{ \frac{11}{126} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{5})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 14x+\frac{28}{5}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{+196} & = & \color{red}{105x} +40 \\\Leftrightarrow & 490x \color{red}{+196} \color{blue}{-196} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-196} \\\Leftrightarrow & 490x-105x& = & 40-196 \\\Leftrightarrow & \color{red}{385} x& = & -156 \\\Leftrightarrow & x = \frac{-156}{385} & & \\ & V = \left\{ \frac{-156}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 2x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 2x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{14x} +4 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{-14x} & = & \color{red}{14x} +4 \color{blue}{-14x} \color{blue}{-6} \\\Leftrightarrow & 63x-14x& = & 4-6 \\\Leftrightarrow & \color{red}{49} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{49} & & \\ & V = \left\{ \frac{-2}{49} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{+8} & = & \color{red}{50x} +3 \\\Leftrightarrow & -40x \color{red}{+8} \color{blue}{-8} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{-8} \\\Leftrightarrow & -40x-50x& = & 3-8 \\\Leftrightarrow & \color{red}{-90} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-90} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-189} & = & \color{red}{-216x} +80 \\\Leftrightarrow & -1008x \color{red}{-189} \color{blue}{+189} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{+189} \\\Leftrightarrow & -1008x+216x& = & 80+189 \\\Leftrightarrow & \color{red}{-792} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-792} & & \\\Leftrightarrow & x = \frac{-269}{792} & & \\ & V = \left\{ \frac{-269}{792} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+66} & = & \color{red}{-385x} +15 \\\Leftrightarrow & -330x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +15 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & -330x+385x& = & 15-66 \\\Leftrightarrow & \color{red}{55} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{55} & & \\ & V = \left\{ \frac{-51}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{3})& = & 9x+\frac{4}{7} \\\Leftrightarrow & 14x-\frac{35}{3}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{-245} & = & \color{red}{189x} +12 \\\Leftrightarrow & 294x \color{red}{-245} \color{blue}{+245} \color{blue}{-189x} & = & \color{red}{189x} +12 \color{blue}{-189x} \color{blue}{+245} \\\Leftrightarrow & 294x-189x& = & 12+245 \\\Leftrightarrow & \color{red}{105} x& = & 257 \\\Leftrightarrow & x = \frac{257}{105} & & \\ & V = \left\{ \frac{257}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{9})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{+20} & = & \color{red}{63x} +24 \\\Leftrightarrow & 135x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & 135x-63x& = & 24-20 \\\Leftrightarrow & \color{red}{72} x& = & 4 \\\Leftrightarrow & x = \frac{4}{72} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)