Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{-40x} +15 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{+40x} & = & \color{red}{-40x} +15 \color{blue}{+40x} \color{blue}{-24} \\\Leftrightarrow & -150x+40x& = & 15-24 \\\Leftrightarrow & \color{red}{-110} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-110} & & \\\Leftrightarrow & x = \frac{9}{110} & & \\ & V = \left\{ \frac{9}{110} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{9})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{28}{9}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{+308} & = & \color{red}{-792x} +54 \\\Leftrightarrow & -2079x \color{red}{+308} \color{blue}{-308} \color{blue}{+792x} & = & \color{red}{-792x} +54 \color{blue}{+792x} \color{blue}{-308} \\\Leftrightarrow & -2079x+792x& = & 54-308 \\\Leftrightarrow & \color{red}{-1287} x& = & -254 \\\Leftrightarrow & x = \frac{-254}{-1287} & & \\\Leftrightarrow & x = \frac{254}{1287} & & \\ & V = \left\{ \frac{254}{1287} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{30}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+90} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 396x \color{red}{+90} \color{blue}{-90} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-90} \\\Leftrightarrow & 396x+165x& = & 22-90 \\\Leftrightarrow & \color{red}{561} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{561} & & \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 28x+\frac{14}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+14} & = & \color{red}{27x} +12 \\\Leftrightarrow & 252x \color{red}{+14} \color{blue}{-14} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{-14} \\\Leftrightarrow & 252x-27x& = & 12-14 \\\Leftrightarrow & \color{red}{225} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{225} & & \\ & V = \left\{ \frac{-2}{225} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x-\frac{12}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-12} & = & \color{red}{55x} +6 \\\Leftrightarrow & 198x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & 198x-55x& = & 6+12 \\\Leftrightarrow & \color{red}{143} x& = & 18 \\\Leftrightarrow & x = \frac{18}{143} & & \\ & V = \left\{ \frac{18}{143} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{+180} & = & \color{red}{-294x} +49 \\\Leftrightarrow & -1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+294x} & = & \color{red}{-294x} +49 \color{blue}{+294x} \color{blue}{-180} \\\Leftrightarrow & -1260x+294x& = & 49-180 \\\Leftrightarrow & \color{red}{-966} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-966} & & \\\Leftrightarrow & x = \frac{131}{966} & & \\ & V = \left\{ \frac{131}{966} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{147x} +27 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{-147x} & = & \color{red}{147x} +27 \color{blue}{-147x} \color{blue}{+140} \\\Leftrightarrow & -420x-147x& = & 27+140 \\\Leftrightarrow & \color{red}{-567} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-567} & & \\\Leftrightarrow & x = \frac{-167}{567} & & \\ & V = \left\{ \frac{-167}{567} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{12})& = & 8x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{35}{12}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2940}{ \color{blue}{84} }x+ \frac{245}{ \color{blue}{84} })& = & (\frac{672}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2940x \color{red}{+245} & = & \color{red}{672x} +120 \\\Leftrightarrow & 2940x \color{red}{+245} \color{blue}{-245} \color{blue}{-672x} & = & \color{red}{672x} +120 \color{blue}{-672x} \color{blue}{-245} \\\Leftrightarrow & 2940x-672x& = & 120-245 \\\Leftrightarrow & \color{red}{2268} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{2268} & & \\ & V = \left\{ \frac{-125}{2268} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{12}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-48} & = & \color{red}{396x} +33 \\\Leftrightarrow & 352x \color{red}{-48} \color{blue}{+48} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{+48} \\\Leftrightarrow & 352x-396x& = & 33+48 \\\Leftrightarrow & \color{red}{-44} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-44} & & \\\Leftrightarrow & x = \frac{-81}{44} & & \\ & V = \left\{ \frac{-81}{44} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-99} \\\Leftrightarrow & -660x-275x& = & 30-99 \\\Leftrightarrow & \color{red}{-935} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-935} & & \\\Leftrightarrow & x = \frac{69}{935} & & \\ & V = \left\{ \frac{69}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{11})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{25}{11}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{175}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-175} & = & \color{red}{231x} +110 \\\Leftrightarrow & -1540x \color{red}{-175} \color{blue}{+175} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+175} \\\Leftrightarrow & -1540x-231x& = & 110+175 \\\Leftrightarrow & \color{red}{-1771} x& = & 285 \\\Leftrightarrow & x = \frac{285}{-1771} & & \\\Leftrightarrow & x = \frac{-285}{1771} & & \\ & V = \left\{ \frac{-285}{1771} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{7}{10} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{+105} & = & \color{red}{120x} +28 \\\Leftrightarrow & 560x \color{red}{+105} \color{blue}{-105} \color{blue}{-120x} & = & \color{red}{120x} +28 \color{blue}{-120x} \color{blue}{-105} \\\Leftrightarrow & 560x-120x& = & 28-105 \\\Leftrightarrow & \color{red}{440} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{440} & & \\\Leftrightarrow & x = \frac{-7}{40} & & \\ & V = \left\{ \frac{-7}{40} \right\} & \\\end{align}\)