Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 28x+\frac{35}{4}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x+ \frac{385}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{28}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{+385} & = & \color{red}{220x} +28 \\\Leftrightarrow & 1232x \color{red}{+385} \color{blue}{-385} \color{blue}{-220x} & = & \color{red}{220x} +28 \color{blue}{-220x} \color{blue}{-385} \\\Leftrightarrow & 1232x-220x& = & 28-385 \\\Leftrightarrow & \color{red}{1012} x& = & -357 \\\Leftrightarrow & x = \frac{-357}{1012} & & \\ & V = \left\{ \frac{-357}{1012} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{8}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-32} & = & \color{red}{308x} +33 \\\Leftrightarrow & 352x \color{red}{-32} \color{blue}{+32} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{+32} \\\Leftrightarrow & 352x-308x& = & 33+32 \\\Leftrightarrow & \color{red}{44} x& = & 65 \\\Leftrightarrow & x = \frac{65}{44} & & \\ & V = \left\{ \frac{65}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+12} & = & \color{red}{25x} +8 \\\Leftrightarrow & -45x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -45x-25x& = & 8-12 \\\Leftrightarrow & \color{red}{-70} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-70} & & \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{6}{11}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-440}{ \color{blue}{110} }x- \frac{60}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -440x \color{red}{-60} & = & \color{red}{990x} +33 \\\Leftrightarrow & -440x \color{red}{-60} \color{blue}{+60} \color{blue}{-990x} & = & \color{red}{990x} +33 \color{blue}{-990x} \color{blue}{+60} \\\Leftrightarrow & -440x-990x& = & 33+60 \\\Leftrightarrow & \color{red}{-1430} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-1430} & & \\\Leftrightarrow & x = \frac{-93}{1430} & & \\ & V = \left\{ \frac{-93}{1430} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{18}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{54}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{147x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+54} \\\Leftrightarrow & 504x-147x& = & 14+54 \\\Leftrightarrow & \color{red}{357} x& = & 68 \\\Leftrightarrow & x = \frac{68}{357} & & \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{105x} +6 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -150x-105x& = & 6-50 \\\Leftrightarrow & \color{red}{-255} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-255} & & \\\Leftrightarrow & x = \frac{44}{255} & & \\ & V = \left\{ \frac{44}{255} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 2x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+66} & = & \color{red}{154x} +70 \\\Leftrightarrow & 1155x \color{red}{+66} \color{blue}{-66} \color{blue}{-154x} & = & \color{red}{154x} +70 \color{blue}{-154x} \color{blue}{-66} \\\Leftrightarrow & 1155x-154x& = & 70-66 \\\Leftrightarrow & \color{red}{1001} x& = & 4 \\\Leftrightarrow & x = \frac{4}{1001} & & \\ & V = \left\{ \frac{4}{1001} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{3})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -14x-\frac{7}{3}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{21}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-21} & = & \color{red}{27x} +2 \\\Leftrightarrow & -126x \color{red}{-21} \color{blue}{+21} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+21} \\\Leftrightarrow & -126x-27x& = & 2+21 \\\Leftrightarrow & \color{red}{-153} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-153} & & \\\Leftrightarrow & x = \frac{-23}{153} & & \\ & V = \left\{ \frac{-23}{153} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{-180} & = & \color{red}{294x} +35 \\\Leftrightarrow & 1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{+180} \\\Leftrightarrow & 1260x-294x& = & 35+180 \\\Leftrightarrow & \color{red}{966} x& = & 215 \\\Leftrightarrow & x = \frac{215}{966} & & \\ & V = \left\{ \frac{215}{966} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-36} & = & \color{red}{-45x} +50 \\\Leftrightarrow & 240x \color{red}{-36} \color{blue}{+36} \color{blue}{+45x} & = & \color{red}{-45x} +50 \color{blue}{+45x} \color{blue}{+36} \\\Leftrightarrow & 240x+45x& = & 50+36 \\\Leftrightarrow & \color{red}{285} x& = & 86 \\\Leftrightarrow & x = \frac{86}{285} & & \\ & V = \left\{ \frac{86}{285} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-28} & = & \color{red}{-54x} +15 \\\Leftrightarrow & 168x \color{red}{-28} \color{blue}{+28} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{+28} \\\Leftrightarrow & 168x+54x& = & 15+28 \\\Leftrightarrow & \color{red}{222} x& = & 43 \\\Leftrightarrow & x = \frac{43}{222} & & \\ & V = \left\{ \frac{43}{222} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{3})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -10x+\frac{8}{3}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+64} & = & \color{red}{168x} +9 \\\Leftrightarrow & -240x \color{red}{+64} \color{blue}{-64} \color{blue}{-168x} & = & \color{red}{168x} +9 \color{blue}{-168x} \color{blue}{-64} \\\Leftrightarrow & -240x-168x& = & 9-64 \\\Leftrightarrow & \color{red}{-408} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-408} & & \\\Leftrightarrow & x = \frac{55}{408} & & \\ & V = \left\{ \frac{55}{408} \right\} & \\\end{align}\)