Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{-96x} +64 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{+96x} & = & \color{red}{-96x} +64 \color{blue}{+96x} \color{blue}{+63} \\\Leftrightarrow & -840x+96x& = & 64+63 \\\Leftrightarrow & \color{red}{-744} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-744} & & \\\Leftrightarrow & x = \frac{-127}{744} & & \\ & V = \left\{ \frac{-127}{744} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+24} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -210x \color{red}{+24} \color{blue}{-24} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{-24} \\\Leftrightarrow & -210x+49x& = & 4-24 \\\Leftrightarrow & \color{red}{-161} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-161} & & \\\Leftrightarrow & x = \frac{20}{161} & & \\ & V = \left\{ \frac{20}{161} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{2})& = & -8x+\frac{3}{2} \\\Leftrightarrow & 35x-\frac{35}{2}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{70}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-16}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 70x \color{red}{-35} & = & \color{red}{-16x} +3 \\\Leftrightarrow & 70x \color{red}{-35} \color{blue}{+35} \color{blue}{+16x} & = & \color{red}{-16x} +3 \color{blue}{+16x} \color{blue}{+35} \\\Leftrightarrow & 70x+16x& = & 3+35 \\\Leftrightarrow & \color{red}{86} x& = & 38 \\\Leftrightarrow & x = \frac{38}{86} & & \\\Leftrightarrow & x = \frac{19}{43} & & \\ & V = \left\{ \frac{19}{43} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -4x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-75} & = & \color{red}{-80x} +18 \\\Leftrightarrow & -300x \color{red}{-75} \color{blue}{+75} \color{blue}{+80x} & = & \color{red}{-80x} +18 \color{blue}{+80x} \color{blue}{+75} \\\Leftrightarrow & -300x+80x& = & 18+75 \\\Leftrightarrow & \color{red}{-220} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-220} & & \\\Leftrightarrow & x = \frac{-93}{220} & & \\ & V = \left\{ \frac{-93}{220} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{7})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -14x+4& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{20}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+20} & = & \color{red}{15x} +2 \\\Leftrightarrow & -70x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & -70x-15x& = & 2-20 \\\Leftrightarrow & \color{red}{-85} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-85} & & \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 15x-\frac{6}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{70x} +25 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & 150x-70x& = & 25+12 \\\Leftrightarrow & \color{red}{80} x& = & 37 \\\Leftrightarrow & x = \frac{37}{80} & & \\ & V = \left\{ \frac{37}{80} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+24} & = & \color{red}{-112x} +21 \\\Leftrightarrow & -420x \color{red}{+24} \color{blue}{-24} \color{blue}{+112x} & = & \color{red}{-112x} +21 \color{blue}{+112x} \color{blue}{-24} \\\Leftrightarrow & -420x+112x& = & 21-24 \\\Leftrightarrow & \color{red}{-308} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-308} & & \\\Leftrightarrow & x = \frac{3}{308} & & \\ & V = \left\{ \frac{3}{308} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{-63x} +9 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & -420x+63x& = & 9-140 \\\Leftrightarrow & \color{red}{-357} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-357} & & \\\Leftrightarrow & x = \frac{131}{357} & & \\ & V = \left\{ \frac{131}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{3})& = & -2x+\frac{5}{2} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -2x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+40} & = & \color{red}{-12x} +15 \\\Leftrightarrow & 150x \color{red}{+40} \color{blue}{-40} \color{blue}{+12x} & = & \color{red}{-12x} +15 \color{blue}{+12x} \color{blue}{-40} \\\Leftrightarrow & 150x+12x& = & 15-40 \\\Leftrightarrow & \color{red}{162} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{162} & & \\ & V = \left\{ \frac{-25}{162} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{+96} & = & \color{red}{378x} +35 \\\Leftrightarrow & -840x \color{red}{+96} \color{blue}{-96} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{-96} \\\Leftrightarrow & -840x-378x& = & 35-96 \\\Leftrightarrow & \color{red}{-1218} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1218} & & \\\Leftrightarrow & x = \frac{61}{1218} & & \\ & V = \left\{ \frac{61}{1218} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+20} & = & \color{red}{126x} +21 \\\Leftrightarrow & 350x \color{red}{+20} \color{blue}{-20} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{-20} \\\Leftrightarrow & 350x-126x& = & 21-20 \\\Leftrightarrow & \color{red}{224} x& = & 1 \\\Leftrightarrow & x = \frac{1}{224} & & \\ & V = \left\{ \frac{1}{224} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{9}{5} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{175x} +63 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +63 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & -315x-175x& = & 63+30 \\\Leftrightarrow & \color{red}{-490} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-490} & & \\\Leftrightarrow & x = \frac{-93}{490} & & \\ & V = \left\{ \frac{-93}{490} \right\} & \\\end{align}\)