Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+56} & = & \color{red}{105x} +6 \\\Leftrightarrow & 336x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & 336x-105x& = & 6-56 \\\Leftrightarrow & \color{red}{231} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{231} & & \\ & V = \left\{ \frac{-50}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{9})& = & 6x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{25}{9}& = & 6x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x+ \frac{25}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+25} & = & \color{red}{54x} +12 \\\Leftrightarrow & 225x \color{red}{+25} \color{blue}{-25} \color{blue}{-54x} & = & \color{red}{54x} +12 \color{blue}{-54x} \color{blue}{-25} \\\Leftrightarrow & 225x-54x& = & 12-25 \\\Leftrightarrow & \color{red}{171} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{171} & & \\ & V = \left\{ \frac{-13}{171} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{+80} & = & \color{red}{60x} +27 \\\Leftrightarrow & -144x \color{red}{+80} \color{blue}{-80} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{-80} \\\Leftrightarrow & -144x-60x& = & 27-80 \\\Leftrightarrow & \color{red}{-204} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-204} & & \\\Leftrightarrow & x = \frac{53}{204} & & \\ & V = \left\{ \frac{53}{204} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -168x \color{red}{+21} & = & \color{red}{-64x} +20 \\\Leftrightarrow & -168x \color{red}{+21} \color{blue}{-21} \color{blue}{+64x} & = & \color{red}{-64x} +20 \color{blue}{+64x} \color{blue}{-21} \\\Leftrightarrow & -168x+64x& = & 20-21 \\\Leftrightarrow & \color{red}{-104} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-104} & & \\\Leftrightarrow & x = \frac{1}{104} & & \\ & V = \left\{ \frac{1}{104} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & 8x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+18} & = & \color{red}{168x} +70 \\\Leftrightarrow & 315x \color{red}{+18} \color{blue}{-18} \color{blue}{-168x} & = & \color{red}{168x} +70 \color{blue}{-168x} \color{blue}{-18} \\\Leftrightarrow & 315x-168x& = & 70-18 \\\Leftrightarrow & \color{red}{147} x& = & 52 \\\Leftrightarrow & x = \frac{52}{147} & & \\ & V = \left\{ \frac{52}{147} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-315x} +20 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+108} \\\Leftrightarrow & 540x+315x& = & 20+108 \\\Leftrightarrow & \color{red}{855} x& = & 128 \\\Leftrightarrow & x = \frac{128}{855} & & \\ & V = \left\{ \frac{128}{855} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+40} & = & \color{red}{18x} +21 \\\Leftrightarrow & 48x \color{red}{+40} \color{blue}{-40} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{-40} \\\Leftrightarrow & 48x-18x& = & 21-40 \\\Leftrightarrow & \color{red}{30} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{30} & & \\ & V = \left\{ \frac{-19}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{81x} +6 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -72x-81x& = & 6-8 \\\Leftrightarrow & \color{red}{-153} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-153} & & \\\Leftrightarrow & x = \frac{2}{153} & & \\ & V = \left\{ \frac{2}{153} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 4x+\frac{8}{9} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+42} & = & \color{red}{36x} +8 \\\Leftrightarrow & -315x \color{red}{+42} \color{blue}{-42} \color{blue}{-36x} & = & \color{red}{36x} +8 \color{blue}{-36x} \color{blue}{-42} \\\Leftrightarrow & -315x-36x& = & 8-42 \\\Leftrightarrow & \color{red}{-351} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-351} & & \\\Leftrightarrow & x = \frac{34}{351} & & \\ & V = \left\{ \frac{34}{351} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{9})& = & 2x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{35}{9}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x+ \frac{175}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{+175} & = & \color{red}{90x} +54 \\\Leftrightarrow & -1260x \color{red}{+175} \color{blue}{-175} \color{blue}{-90x} & = & \color{red}{90x} +54 \color{blue}{-90x} \color{blue}{-175} \\\Leftrightarrow & -1260x-90x& = & 54-175 \\\Leftrightarrow & \color{red}{-1350} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{-1350} & & \\\Leftrightarrow & x = \frac{121}{1350} & & \\ & V = \left\{ \frac{121}{1350} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +21 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 21+50 \\\Leftrightarrow & \color{red}{-105} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-105} & & \\\Leftrightarrow & x = \frac{-71}{105} & & \\ & V = \left\{ \frac{-71}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -14x+\frac{28}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{84}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+84} & = & \color{red}{-99x} +22 \\\Leftrightarrow & -462x \color{red}{+84} \color{blue}{-84} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{-84} \\\Leftrightarrow & -462x+99x& = & 22-84 \\\Leftrightarrow & \color{red}{-363} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-363} & & \\\Leftrightarrow & x = \frac{62}{363} & & \\ & V = \left\{ \frac{62}{363} \right\} & \\\end{align}\)