Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-168}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -168x \color{red}{+60} & = & \color{red}{210x} +49 \\\Leftrightarrow & -168x \color{red}{+60} \color{blue}{-60} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{-60} \\\Leftrightarrow & -168x-210x& = & 49-60 \\\Leftrightarrow & \color{red}{-378} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-378} & & \\\Leftrightarrow & x = \frac{11}{378} & & \\ & V = \left\{ \frac{11}{378} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{35x} +3 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & 60x-35x& = & 3+24 \\\Leftrightarrow & \color{red}{25} x& = & 27 \\\Leftrightarrow & x = \frac{27}{25} & & \\ & V = \left\{ \frac{27}{25} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-900}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-240}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -900x \color{red}{+144} & = & \color{red}{-240x} +35 \\\Leftrightarrow & -900x \color{red}{+144} \color{blue}{-144} \color{blue}{+240x} & = & \color{red}{-240x} +35 \color{blue}{+240x} \color{blue}{-144} \\\Leftrightarrow & -900x+240x& = & 35-144 \\\Leftrightarrow & \color{red}{-660} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-660} & & \\\Leftrightarrow & x = \frac{109}{660} & & \\ & V = \left\{ \frac{109}{660} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{+75} & = & \color{red}{-100x} +24 \\\Leftrightarrow & -180x \color{red}{+75} \color{blue}{-75} \color{blue}{+100x} & = & \color{red}{-100x} +24 \color{blue}{+100x} \color{blue}{-75} \\\Leftrightarrow & -180x+100x& = & 24-75 \\\Leftrightarrow & \color{red}{-80} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-80} & & \\\Leftrightarrow & x = \frac{51}{80} & & \\ & V = \left\{ \frac{51}{80} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-220} & = & \color{red}{297x} +54 \\\Leftrightarrow & 1980x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +54 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 1980x-297x& = & 54+220 \\\Leftrightarrow & \color{red}{1683} x& = & 274 \\\Leftrightarrow & x = \frac{274}{1683} & & \\ & V = \left\{ \frac{274}{1683} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{11})& = & 2x+\frac{3}{10} \\\Leftrightarrow & 25x+\frac{10}{11}& = & 2x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2750}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{220}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2750x \color{red}{+100} & = & \color{red}{220x} +33 \\\Leftrightarrow & 2750x \color{red}{+100} \color{blue}{-100} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{-100} \\\Leftrightarrow & 2750x-220x& = & 33-100 \\\Leftrightarrow & \color{red}{2530} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{2530} & & \\ & V = \left\{ \frac{-67}{2530} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +9 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 9-24 \\\Leftrightarrow & \color{red}{-70} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-70} & & \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{11})& = & -2x+\frac{3}{7} \\\Leftrightarrow & 35x+\frac{35}{11}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{+245} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 2695x \color{red}{+245} \color{blue}{-245} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-245} \\\Leftrightarrow & 2695x+154x& = & 33-245 \\\Leftrightarrow & \color{red}{2849} x& = & -212 \\\Leftrightarrow & x = \frac{-212}{2849} & & \\ & V = \left\{ \frac{-212}{2849} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-10} & = & \color{red}{-21x} +8 \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & 30x+21x& = & 8+10 \\\Leftrightarrow & \color{red}{51} x& = & 18 \\\Leftrightarrow & x = \frac{18}{51} & & \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-216x} +40 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +40 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & -672x+216x& = & 40-63 \\\Leftrightarrow & \color{red}{-456} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-456} & & \\\Leftrightarrow & x = \frac{23}{456} & & \\ & V = \left\{ \frac{23}{456} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & 3x+\frac{7}{11} \\\Leftrightarrow & -8x-\frac{4}{5}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-44} & = & \color{red}{165x} +35 \\\Leftrightarrow & -440x \color{red}{-44} \color{blue}{+44} \color{blue}{-165x} & = & \color{red}{165x} +35 \color{blue}{-165x} \color{blue}{+44} \\\Leftrightarrow & -440x-165x& = & 35+44 \\\Leftrightarrow & \color{red}{-605} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-605} & & \\\Leftrightarrow & x = \frac{-79}{605} & & \\ & V = \left\{ \frac{-79}{605} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{2})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{25}{2}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+225} & = & \color{red}{126x} +16 \\\Leftrightarrow & 180x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +16 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & 180x-126x& = & 16-225 \\\Leftrightarrow & \color{red}{54} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{54} & & \\ & V = \left\{ \frac{-209}{54} \right\} & \\\end{align}\)