Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-108} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 270x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 270x+225x& = & 25+108 \\\Leftrightarrow & \color{red}{495} x& = & 133 \\\Leftrightarrow & x = \frac{133}{495} & & \\ & V = \left\{ \frac{133}{495} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{9})& = & 6x+\frac{2}{9} \\\Leftrightarrow & 35x+\frac{35}{9}& = & 6x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+35} & = & \color{red}{54x} +2 \\\Leftrightarrow & 315x \color{red}{+35} \color{blue}{-35} \color{blue}{-54x} & = & \color{red}{54x} +2 \color{blue}{-54x} \color{blue}{-35} \\\Leftrightarrow & 315x-54x& = & 2-35 \\\Leftrightarrow & \color{red}{261} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{261} & & \\\Leftrightarrow & x = \frac{-11}{87} & & \\ & V = \left\{ \frac{-11}{87} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 25x-\frac{20}{7}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-60} & = & \color{red}{189x} +14 \\\Leftrightarrow & 525x \color{red}{-60} \color{blue}{+60} \color{blue}{-189x} & = & \color{red}{189x} +14 \color{blue}{-189x} \color{blue}{+60} \\\Leftrightarrow & 525x-189x& = & 14+60 \\\Leftrightarrow & \color{red}{336} x& = & 74 \\\Leftrightarrow & x = \frac{74}{336} & & \\\Leftrightarrow & x = \frac{37}{168} & & \\ & V = \left\{ \frac{37}{168} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+12} & = & \color{red}{126x} +49 \\\Leftrightarrow & 140x \color{red}{+12} \color{blue}{-12} \color{blue}{-126x} & = & \color{red}{126x} +49 \color{blue}{-126x} \color{blue}{-12} \\\Leftrightarrow & 140x-126x& = & 49-12 \\\Leftrightarrow & \color{red}{14} x& = & 37 \\\Leftrightarrow & x = \frac{37}{14} & & \\ & V = \left\{ \frac{37}{14} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-25x} +2 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -60x+25x& = & 2-12 \\\Leftrightarrow & \color{red}{-35} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-35} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x+\frac{9}{10}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{70x} +14 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{-70x} & = & \color{red}{70x} +14 \color{blue}{-70x} \color{blue}{-9} \\\Leftrightarrow & -60x-70x& = & 14-9 \\\Leftrightarrow & \color{red}{-130} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-130} & & \\\Leftrightarrow & x = \frac{-1}{26} & & \\ & V = \left\{ \frac{-1}{26} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+44} & = & \color{red}{-165x} +40 \\\Leftrightarrow & 220x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +40 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & 220x+165x& = & 40-44 \\\Leftrightarrow & \color{red}{385} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{385} & & \\ & V = \left\{ \frac{-4}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 30x-\frac{12}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-24} & = & \color{red}{154x} +55 \\\Leftrightarrow & 660x \color{red}{-24} \color{blue}{+24} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+24} \\\Leftrightarrow & 660x-154x& = & 55+24 \\\Leftrightarrow & \color{red}{506} x& = & 79 \\\Leftrightarrow & x = \frac{79}{506} & & \\ & V = \left\{ \frac{79}{506} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{245x} +49 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{-60} \\\Leftrightarrow & 420x-245x& = & 49-60 \\\Leftrightarrow & \color{red}{175} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{175} & & \\ & V = \left\{ \frac{-11}{175} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 2x+\frac{5}{7} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 2x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+196} & = & \color{red}{70x} +25 \\\Leftrightarrow & 735x \color{red}{+196} \color{blue}{-196} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{-196} \\\Leftrightarrow & 735x-70x& = & 25-196 \\\Leftrightarrow & \color{red}{665} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{665} & & \\\Leftrightarrow & x = \frac{-9}{35} & & \\ & V = \left\{ \frac{-9}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 20x-\frac{10}{3}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+70} \\\Leftrightarrow & 420x+63x& = & 6+70 \\\Leftrightarrow & \color{red}{483} x& = & 76 \\\Leftrightarrow & x = \frac{76}{483} & & \\ & V = \left\{ \frac{76}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{15}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+45} & = & \color{red}{63x} +14 \\\Leftrightarrow & 420x \color{red}{+45} \color{blue}{-45} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{-45} \\\Leftrightarrow & 420x-63x& = & 14-45 \\\Leftrightarrow & \color{red}{357} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{357} & & \\ & V = \left\{ \frac{-31}{357} \right\} & \\\end{align}\)