Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-30} & = & \color{red}{-175x} +56 \\\Leftrightarrow & -420x \color{red}{-30} \color{blue}{+30} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+30} \\\Leftrightarrow & -420x+175x& = & 56+30 \\\Leftrightarrow & \color{red}{-245} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-245} & & \\\Leftrightarrow & x = \frac{-86}{245} & & \\ & V = \left\{ \frac{-86}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+24} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 336x \color{red}{+24} \color{blue}{-24} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-24} \\\Leftrightarrow & 336x+140x& = & 63-24 \\\Leftrightarrow & \color{red}{476} x& = & 39 \\\Leftrightarrow & x = \frac{39}{476} & & \\ & V = \left\{ \frac{39}{476} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{98x} +35 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{+12} \\\Leftrightarrow & 84x-98x& = & 35+12 \\\Leftrightarrow & \color{red}{-14} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-14} & & \\\Leftrightarrow & x = \frac{-47}{14} & & \\ & V = \left\{ \frac{-47}{14} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{-270x} +9 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{-175} \\\Leftrightarrow & 420x+270x& = & 9-175 \\\Leftrightarrow & \color{red}{690} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{690} & & \\\Leftrightarrow & x = \frac{-83}{345} & & \\ & V = \left\{ \frac{-83}{345} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+225} & = & \color{red}{126x} +16 \\\Leftrightarrow & -180x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +16 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & -180x-126x& = & 16-225 \\\Leftrightarrow & \color{red}{-306} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{-306} & & \\\Leftrightarrow & x = \frac{209}{306} & & \\ & V = \left\{ \frac{209}{306} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{81x} +12 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +12 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -36x-81x& = & 12-8 \\\Leftrightarrow & \color{red}{-117} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-117} & & \\\Leftrightarrow & x = \frac{-4}{117} & & \\ & V = \left\{ \frac{-4}{117} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & 8x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{16}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{-15} & = & \color{red}{16x} +3 \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-16x} & = & \color{red}{16x} +3 \color{blue}{-16x} \color{blue}{+15} \\\Leftrightarrow & -30x-16x& = & 3+15 \\\Leftrightarrow & \color{red}{-46} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-46} & & \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{3})& = & -9x+\frac{2}{7} \\\Leftrightarrow & 10x-\frac{4}{3}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-189x} +6 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+189x} & = & \color{red}{-189x} +6 \color{blue}{+189x} \color{blue}{+28} \\\Leftrightarrow & 210x+189x& = & 6+28 \\\Leftrightarrow & \color{red}{399} x& = & 34 \\\Leftrightarrow & x = \frac{34}{399} & & \\ & V = \left\{ \frac{34}{399} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & -120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{5})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 4x-\frac{8}{5}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{-16} & = & \color{red}{-90x} +25 \\\Leftrightarrow & 40x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & 40x+90x& = & 25+16 \\\Leftrightarrow & \color{red}{130} x& = & 41 \\\Leftrightarrow & x = \frac{41}{130} & & \\ & V = \left\{ \frac{41}{130} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{45x} +6 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & -36x-45x& = & 6-8 \\\Leftrightarrow & \color{red}{-81} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-81} & & \\\Leftrightarrow & x = \frac{2}{81} & & \\ & V = \left\{ \frac{2}{81} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+30} & = & \color{red}{105x} +56 \\\Leftrightarrow & -525x \color{red}{+30} \color{blue}{-30} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-30} \\\Leftrightarrow & -525x-105x& = & 56-30 \\\Leftrightarrow & \color{red}{-630} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-630} & & \\\Leftrightarrow & x = \frac{-13}{315} & & \\ & V = \left\{ \frac{-13}{315} \right\} & \\\end{align}\)