Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{3})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -25x-\frac{25}{3}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x- \frac{25}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{-25} & = & \color{red}{-24x} +7 \\\Leftrightarrow & -75x \color{red}{-25} \color{blue}{+25} \color{blue}{+24x} & = & \color{red}{-24x} +7 \color{blue}{+24x} \color{blue}{+25} \\\Leftrightarrow & -75x+24x& = & 7+25 \\\Leftrightarrow & \color{red}{-51} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-51} & & \\\Leftrightarrow & x = \frac{-32}{51} & & \\ & V = \left\{ \frac{-32}{51} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{9})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{+28} \\\Leftrightarrow & 252x+81x& = & 10+28 \\\Leftrightarrow & \color{red}{333} x& = & 38 \\\Leftrightarrow & x = \frac{38}{333} & & \\ & V = \left\{ \frac{38}{333} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{96}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 96x \color{red}{-64} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 96x \color{red}{-64} \color{blue}{+64} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+64} \\\Leftrightarrow & 96x+72x& = & 21+64 \\\Leftrightarrow & \color{red}{168} x& = & 85 \\\Leftrightarrow & x = \frac{85}{168} & & \\ & V = \left\{ \frac{85}{168} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{12}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 12x \color{red}{-8} & = & \color{red}{-9x} +7 \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+9x} & = & \color{red}{-9x} +7 \color{blue}{+9x} \color{blue}{+8} \\\Leftrightarrow & 12x+9x& = & 7+8 \\\Leftrightarrow & \color{red}{21} x& = & 15 \\\Leftrightarrow & x = \frac{15}{21} & & \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-20} & = & \color{red}{98x} +35 \\\Leftrightarrow & -140x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & -140x-98x& = & 35+20 \\\Leftrightarrow & \color{red}{-238} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-238} & & \\\Leftrightarrow & x = \frac{-55}{238} & & \\ & V = \left\{ \frac{-55}{238} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{-63} & = & \color{red}{350x} +100 \\\Leftrightarrow & -630x \color{red}{-63} \color{blue}{+63} \color{blue}{-350x} & = & \color{red}{350x} +100 \color{blue}{-350x} \color{blue}{+63} \\\Leftrightarrow & -630x-350x& = & 100+63 \\\Leftrightarrow & \color{red}{-980} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-980} & & \\\Leftrightarrow & x = \frac{-163}{980} & & \\ & V = \left\{ \frac{-163}{980} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{72x} +80 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{-72x} & = & \color{red}{72x} +80 \color{blue}{-72x} \color{blue}{+63} \\\Leftrightarrow & -840x-72x& = & 80+63 \\\Leftrightarrow & \color{red}{-912} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-912} & & \\\Leftrightarrow & x = \frac{-143}{912} & & \\ & V = \left\{ \frac{-143}{912} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{7})& = & 9x+\frac{7}{9} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-180} & = & \color{red}{567x} +49 \\\Leftrightarrow & -504x \color{red}{-180} \color{blue}{+180} \color{blue}{-567x} & = & \color{red}{567x} +49 \color{blue}{-567x} \color{blue}{+180} \\\Leftrightarrow & -504x-567x& = & 49+180 \\\Leftrightarrow & \color{red}{-1071} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1071} & & \\\Leftrightarrow & x = \frac{-229}{1071} & & \\ & V = \left\{ \frac{-229}{1071} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{9})& = & -4x+\frac{7}{12} \\\Leftrightarrow & 35x+\frac{35}{9}& = & -4x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{-144}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{+140} & = & \color{red}{-144x} +21 \\\Leftrightarrow & 1260x \color{red}{+140} \color{blue}{-140} \color{blue}{+144x} & = & \color{red}{-144x} +21 \color{blue}{+144x} \color{blue}{-140} \\\Leftrightarrow & 1260x+144x& = & 21-140 \\\Leftrightarrow & \color{red}{1404} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{1404} & & \\ & V = \left\{ \frac{-119}{1404} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-88} & = & \color{red}{-891x} +18 \\\Leftrightarrow & -792x \color{red}{-88} \color{blue}{+88} \color{blue}{+891x} & = & \color{red}{-891x} +18 \color{blue}{+891x} \color{blue}{+88} \\\Leftrightarrow & -792x+891x& = & 18+88 \\\Leftrightarrow & \color{red}{99} x& = & 106 \\\Leftrightarrow & x = \frac{106}{99} & & \\ & V = \left\{ \frac{106}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{9})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 8x-\frac{4}{9}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-28} & = & \color{red}{-441x} +81 \\\Leftrightarrow & 504x \color{red}{-28} \color{blue}{+28} \color{blue}{+441x} & = & \color{red}{-441x} +81 \color{blue}{+441x} \color{blue}{+28} \\\Leftrightarrow & 504x+441x& = & 81+28 \\\Leftrightarrow & \color{red}{945} x& = & 109 \\\Leftrightarrow & x = \frac{109}{945} & & \\ & V = \left\{ \frac{109}{945} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{11})& = & 3x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x+ \frac{160}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{+160} & = & \color{red}{330x} +33 \\\Leftrightarrow & -2200x \color{red}{+160} \color{blue}{-160} \color{blue}{-330x} & = & \color{red}{330x} +33 \color{blue}{-330x} \color{blue}{-160} \\\Leftrightarrow & -2200x-330x& = & 33-160 \\\Leftrightarrow & \color{red}{-2530} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-2530} & & \\\Leftrightarrow & x = \frac{127}{2530} & & \\ & V = \left\{ \frac{127}{2530} \right\} & \\\end{align}\)