Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{-160} & = & \color{red}{168x} +27 \\\Leftrightarrow & 480x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +27 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & 480x-168x& = & 27+160 \\\Leftrightarrow & \color{red}{312} x& = & 187 \\\Leftrightarrow & x = \frac{187}{312} & & \\ & V = \left\{ \frac{187}{312} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{18}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+54} & = & \color{red}{-75x} +35 \\\Leftrightarrow & 180x \color{red}{+54} \color{blue}{-54} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{-54} \\\Leftrightarrow & 180x+75x& = & 35-54 \\\Leftrightarrow & \color{red}{255} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{255} & & \\ & V = \left\{ \frac{-19}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{99x} +77 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{-99x} & = & \color{red}{99x} +77 \color{blue}{-99x} \color{blue}{-60} \\\Leftrightarrow & 660x-99x& = & 77-60 \\\Leftrightarrow & \color{red}{561} x& = & 17 \\\Leftrightarrow & x = \frac{17}{561} & & \\\Leftrightarrow & x = \frac{1}{33} & & \\ & V = \left\{ \frac{1}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{+15} & = & \color{red}{-20x} +18 \\\Leftrightarrow & 24x \color{red}{+15} \color{blue}{-15} \color{blue}{+20x} & = & \color{red}{-20x} +18 \color{blue}{+20x} \color{blue}{-15} \\\Leftrightarrow & 24x+20x& = & 18-15 \\\Leftrightarrow & \color{red}{44} x& = & 3 \\\Leftrightarrow & x = \frac{3}{44} & & \\ & V = \left\{ \frac{3}{44} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{8})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{+63} & = & \color{red}{-48x} +16 \\\Leftrightarrow & 840x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 840x+48x& = & 16-63 \\\Leftrightarrow & \color{red}{888} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{888} & & \\ & V = \left\{ \frac{-47}{888} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -90x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -90x-105x& = & 50-36 \\\Leftrightarrow & \color{red}{-195} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-195} & & \\\Leftrightarrow & x = \frac{-14}{195} & & \\ & V = \left\{ \frac{-14}{195} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{4})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{25}{4}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{75}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-75} & = & \color{red}{-84x} +8 \\\Leftrightarrow & 180x \color{red}{-75} \color{blue}{+75} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{+75} \\\Leftrightarrow & 180x+84x& = & 8+75 \\\Leftrightarrow & \color{red}{264} x& = & 83 \\\Leftrightarrow & x = \frac{83}{264} & & \\ & V = \left\{ \frac{83}{264} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{50x} +25 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{+36} \\\Leftrightarrow & 120x-50x& = & 25+36 \\\Leftrightarrow & \color{red}{70} x& = & 61 \\\Leftrightarrow & x = \frac{61}{70} & & \\ & V = \left\{ \frac{61}{70} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{105x} +6 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 168x-105x& = & 6-28 \\\Leftrightarrow & \color{red}{63} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{63} & & \\ & V = \left\{ \frac{-22}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -3x+\frac{9}{5} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+12} & = & \color{red}{-15x} +9 \\\Leftrightarrow & -40x \color{red}{+12} \color{blue}{-12} \color{blue}{+15x} & = & \color{red}{-15x} +9 \color{blue}{+15x} \color{blue}{-12} \\\Leftrightarrow & -40x+15x& = & 9-12 \\\Leftrightarrow & \color{red}{-25} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-25} & & \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{9})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -21x+\frac{28}{9}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1323}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1323x \color{red}{+196} & = & \color{red}{-504x} +36 \\\Leftrightarrow & -1323x \color{red}{+196} \color{blue}{-196} \color{blue}{+504x} & = & \color{red}{-504x} +36 \color{blue}{+504x} \color{blue}{-196} \\\Leftrightarrow & -1323x+504x& = & 36-196 \\\Leftrightarrow & \color{red}{-819} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{-819} & & \\\Leftrightarrow & x = \frac{160}{819} & & \\ & V = \left\{ \frac{160}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -6x+\frac{5}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -6x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-126x} +35 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{-30} \\\Leftrightarrow & 525x+126x& = & 35-30 \\\Leftrightarrow & \color{red}{651} x& = & 5 \\\Leftrightarrow & x = \frac{5}{651} & & \\ & V = \left\{ \frac{5}{651} \right\} & \\\end{align}\)