Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{11})& = & 4x+\frac{10}{9} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{+270} & = & \color{red}{396x} +110 \\\Leftrightarrow & -1782x \color{red}{+270} \color{blue}{-270} \color{blue}{-396x} & = & \color{red}{396x} +110 \color{blue}{-396x} \color{blue}{-270} \\\Leftrightarrow & -1782x-396x& = & 110-270 \\\Leftrightarrow & \color{red}{-2178} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{-2178} & & \\\Leftrightarrow & x = \frac{80}{1089} & & \\ & V = \left\{ \frac{80}{1089} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & 3x+\frac{3}{4} \\\Leftrightarrow & -14x+\frac{35}{9}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+140} & = & \color{red}{108x} +27 \\\Leftrightarrow & -504x \color{red}{+140} \color{blue}{-140} \color{blue}{-108x} & = & \color{red}{108x} +27 \color{blue}{-108x} \color{blue}{-140} \\\Leftrightarrow & -504x-108x& = & 27-140 \\\Leftrightarrow & \color{red}{-612} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-612} & & \\\Leftrightarrow & x = \frac{113}{612} & & \\ & V = \left\{ \frac{113}{612} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -315x+175x& = & 10+84 \\\Leftrightarrow & \color{red}{-140} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-140} & & \\\Leftrightarrow & x = \frac{-47}{70} & & \\ & V = \left\{ \frac{-47}{70} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{+70} & = & \color{red}{-75x} +12 \\\Leftrightarrow & 210x \color{red}{+70} \color{blue}{-70} \color{blue}{+75x} & = & \color{red}{-75x} +12 \color{blue}{+75x} \color{blue}{-70} \\\Leftrightarrow & 210x+75x& = & 12-70 \\\Leftrightarrow & \color{red}{285} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{285} & & \\ & V = \left\{ \frac{-58}{285} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & 1320x+275x& = & 66+90 \\\Leftrightarrow & \color{red}{1595} x& = & 156 \\\Leftrightarrow & x = \frac{156}{1595} & & \\ & V = \left\{ \frac{156}{1595} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 6x+\frac{6}{11} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{66x} +6 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{+18} \\\Leftrightarrow & -198x-66x& = & 6+18 \\\Leftrightarrow & \color{red}{-264} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-264} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{-440x} +10 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{+440x} & = & \color{red}{-440x} +10 \color{blue}{+440x} \color{blue}{-66} \\\Leftrightarrow & -825x+440x& = & 10-66 \\\Leftrightarrow & \color{red}{-385} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-385} & & \\\Leftrightarrow & x = \frac{8}{55} & & \\ & V = \left\{ \frac{8}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{8})& = & -8x+\frac{2}{7} \\\Leftrightarrow & 35x+\frac{35}{8}& = & -8x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x+ \frac{245}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{+245} & = & \color{red}{-448x} +16 \\\Leftrightarrow & 1960x \color{red}{+245} \color{blue}{-245} \color{blue}{+448x} & = & \color{red}{-448x} +16 \color{blue}{+448x} \color{blue}{-245} \\\Leftrightarrow & 1960x+448x& = & 16-245 \\\Leftrightarrow & \color{red}{2408} x& = & -229 \\\Leftrightarrow & x = \frac{-229}{2408} & & \\ & V = \left\{ \frac{-229}{2408} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-14} & = & \color{red}{-27x} +2 \\\Leftrightarrow & 84x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & 84x+27x& = & 2+14 \\\Leftrightarrow & \color{red}{111} x& = & 16 \\\Leftrightarrow & x = \frac{16}{111} & & \\ & V = \left\{ \frac{16}{111} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{8}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{75x} +6 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{+40} \\\Leftrightarrow & -180x-75x& = & 6+40 \\\Leftrightarrow & \color{red}{-255} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-255} & & \\\Leftrightarrow & x = \frac{-46}{255} & & \\ & V = \left\{ \frac{-46}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+168} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 630x \color{red}{+168} \color{blue}{-168} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-168} \\\Leftrightarrow & 630x+175x& = & 15-168 \\\Leftrightarrow & \color{red}{805} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{805} & & \\ & V = \left\{ \frac{-153}{805} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{504}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 504x \color{red}{-72} & = & \color{red}{420x} +35 \\\Leftrightarrow & 504x \color{red}{-72} \color{blue}{+72} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{+72} \\\Leftrightarrow & 504x-420x& = & 35+72 \\\Leftrightarrow & \color{red}{84} x& = & 107 \\\Leftrightarrow & x = \frac{107}{84} & & \\ & V = \left\{ \frac{107}{84} \right\} & \\\end{align}\)