Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{10})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{21}{10}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{63}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{20}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-63} & = & \color{red}{-270x} +20 \\\Leftrightarrow & 1050x \color{red}{-63} \color{blue}{+63} \color{blue}{+270x} & = & \color{red}{-270x} +20 \color{blue}{+270x} \color{blue}{+63} \\\Leftrightarrow & 1050x+270x& = & 20+63 \\\Leftrightarrow & \color{red}{1320} x& = & 83 \\\Leftrightarrow & x = \frac{83}{1320} & & \\ & V = \left\{ \frac{83}{1320} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{36x} +16 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{+45} \\\Leftrightarrow & -240x-36x& = & 16+45 \\\Leftrightarrow & \color{red}{-276} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-276} & & \\\Leftrightarrow & x = \frac{-61}{276} & & \\ & V = \left\{ \frac{-61}{276} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{2})& = & -8x+\frac{9}{7} \\\Leftrightarrow & 9x-\frac{15}{2}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{126}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 126x \color{red}{-105} & = & \color{red}{-112x} +18 \\\Leftrightarrow & 126x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +18 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & 126x+112x& = & 18+105 \\\Leftrightarrow & \color{red}{238} x& = & 123 \\\Leftrightarrow & x = \frac{123}{238} & & \\ & V = \left\{ \frac{123}{238} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{15}{8}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{+75} & = & \color{red}{-320x} +48 \\\Leftrightarrow & -600x \color{red}{+75} \color{blue}{-75} \color{blue}{+320x} & = & \color{red}{-320x} +48 \color{blue}{+320x} \color{blue}{-75} \\\Leftrightarrow & -600x+320x& = & 48-75 \\\Leftrightarrow & \color{red}{-280} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-280} & & \\\Leftrightarrow & x = \frac{27}{280} & & \\ & V = \left\{ \frac{27}{280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+175} & = & \color{red}{-567x} +18 \\\Leftrightarrow & -1260x \color{red}{+175} \color{blue}{-175} \color{blue}{+567x} & = & \color{red}{-567x} +18 \color{blue}{+567x} \color{blue}{-175} \\\Leftrightarrow & -1260x+567x& = & 18-175 \\\Leftrightarrow & \color{red}{-693} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-693} & & \\\Leftrightarrow & x = \frac{157}{693} & & \\ & V = \left\{ \frac{157}{693} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{2})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{15}{2}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{30}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{4}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 30x \color{red}{-15} & = & \color{red}{4x} +9 \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = & \color{red}{4x} +9 \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 30x-4x& = & 9+15 \\\Leftrightarrow & \color{red}{26} x& = & 24 \\\Leftrightarrow & x = \frac{24}{26} & & \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & 2x+\frac{8}{3} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{6x} +8 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{-6x} & = & \color{red}{6x} +8 \color{blue}{-6x} \color{blue}{+28} \\\Leftrightarrow & -84x-6x& = & 8+28 \\\Leftrightarrow & \color{red}{-90} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-90} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+20} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 84x \color{red}{+20} \color{blue}{-20} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-20} \\\Leftrightarrow & 84x+35x& = & 3-20 \\\Leftrightarrow & \color{red}{119} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{119} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{6}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-54} & = & \color{red}{-225x} +40 \\\Leftrightarrow & -540x \color{red}{-54} \color{blue}{+54} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+54} \\\Leftrightarrow & -540x+225x& = & 40+54 \\\Leftrightarrow & \color{red}{-315} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-315} & & \\\Leftrightarrow & x = \frac{-94}{315} & & \\ & V = \left\{ \frac{-94}{315} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-176} & = & \color{red}{-231x} +63 \\\Leftrightarrow & -616x \color{red}{-176} \color{blue}{+176} \color{blue}{+231x} & = & \color{red}{-231x} +63 \color{blue}{+231x} \color{blue}{+176} \\\Leftrightarrow & -616x+231x& = & 63+176 \\\Leftrightarrow & \color{red}{-385} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-385} & & \\\Leftrightarrow & x = \frac{-239}{385} & & \\ & V = \left\{ \frac{-239}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 8x+\frac{16}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{176}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+176} & = & \color{red}{275x} +50 \\\Leftrightarrow & 440x \color{red}{+176} \color{blue}{-176} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-176} \\\Leftrightarrow & 440x-275x& = & 50-176 \\\Leftrightarrow & \color{red}{165} x& = & -126 \\\Leftrightarrow & x = \frac{-126}{165} & & \\\Leftrightarrow & x = \frac{-42}{55} & & \\ & V = \left\{ \frac{-42}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{+12} & = & \color{red}{-110x} +55 \\\Leftrightarrow & 132x \color{red}{+12} \color{blue}{-12} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{-12} \\\Leftrightarrow & 132x+110x& = & 55-12 \\\Leftrightarrow & \color{red}{242} x& = & 43 \\\Leftrightarrow & x = \frac{43}{242} & & \\ & V = \left\{ \frac{43}{242} \right\} & \\\end{align}\)