Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{20}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{40}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-40} & = & \color{red}{-110x} +55 \\\Leftrightarrow & -264x \color{red}{-40} \color{blue}{+40} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{+40} \\\Leftrightarrow & -264x+110x& = & 55+40 \\\Leftrightarrow & \color{red}{-154} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-154} & & \\\Leftrightarrow & x = \frac{-95}{154} & & \\ & V = \left\{ \frac{-95}{154} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+12} & = & \color{red}{45x} +6 \\\Leftrightarrow & 40x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 40x-45x& = & 6-12 \\\Leftrightarrow & \color{red}{-5} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-5} & & \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{135x} +10 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{+12} \\\Leftrightarrow & -60x-135x& = & 10+12 \\\Leftrightarrow & \color{red}{-195} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-195} & & \\\Leftrightarrow & x = \frac{-22}{195} & & \\ & V = \left\{ \frac{-22}{195} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{4})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -14x-\frac{35}{4}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-392}{ \color{blue}{28} }x- \frac{245}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -392x \color{red}{-245} & = & \color{red}{84x} +40 \\\Leftrightarrow & -392x \color{red}{-245} \color{blue}{+245} \color{blue}{-84x} & = & \color{red}{84x} +40 \color{blue}{-84x} \color{blue}{+245} \\\Leftrightarrow & -392x-84x& = & 40+245 \\\Leftrightarrow & \color{red}{-476} x& = & 285 \\\Leftrightarrow & x = \frac{285}{-476} & & \\\Leftrightarrow & x = \frac{-285}{476} & & \\ & V = \left\{ \frac{-285}{476} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{12}{7}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+36} & = & \color{red}{-84x} +28 \\\Leftrightarrow & -315x \color{red}{+36} \color{blue}{-36} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{-36} \\\Leftrightarrow & -315x+84x& = & 28-36 \\\Leftrightarrow & \color{red}{-231} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-231} & & \\\Leftrightarrow & x = \frac{8}{231} & & \\ & V = \left\{ \frac{8}{231} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{9})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 28x-\frac{35}{9}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{-175} & = & \color{red}{405x} +72 \\\Leftrightarrow & 1260x \color{red}{-175} \color{blue}{+175} \color{blue}{-405x} & = & \color{red}{405x} +72 \color{blue}{-405x} \color{blue}{+175} \\\Leftrightarrow & 1260x-405x& = & 72+175 \\\Leftrightarrow & \color{red}{855} x& = & 247 \\\Leftrightarrow & x = \frac{247}{855} & & \\\Leftrightarrow & x = \frac{13}{45} & & \\ & V = \left\{ \frac{13}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{6}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x- \frac{60}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{550x} +33 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+60} \\\Leftrightarrow & 660x-550x& = & 33+60 \\\Leftrightarrow & \color{red}{110} x& = & 93 \\\Leftrightarrow & x = \frac{93}{110} & & \\ & V = \left\{ \frac{93}{110} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2112}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2112x \color{red}{-144} & = & \color{red}{616x} +77 \\\Leftrightarrow & 2112x \color{red}{-144} \color{blue}{+144} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+144} \\\Leftrightarrow & 2112x-616x& = & 77+144 \\\Leftrightarrow & \color{red}{1496} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1496} & & \\\Leftrightarrow & x = \frac{13}{88} & & \\ & V = \left\{ \frac{13}{88} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1584}{ \color{blue}{132} }x- \frac{216}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1584x \color{red}{-216} & = & \color{red}{660x} +77 \\\Leftrightarrow & -1584x \color{red}{-216} \color{blue}{+216} \color{blue}{-660x} & = & \color{red}{660x} +77 \color{blue}{-660x} \color{blue}{+216} \\\Leftrightarrow & -1584x-660x& = & 77+216 \\\Leftrightarrow & \color{red}{-2244} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-2244} & & \\\Leftrightarrow & x = \frac{-293}{2244} & & \\ & V = \left\{ \frac{-293}{2244} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & -9x+\frac{9}{10} \\\Leftrightarrow & 16x-\frac{16}{3}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{480}{ \color{blue}{30} }x- \frac{160}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 480x \color{red}{-160} & = & \color{red}{-270x} +27 \\\Leftrightarrow & 480x \color{red}{-160} \color{blue}{+160} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{+160} \\\Leftrightarrow & 480x+270x& = & 27+160 \\\Leftrightarrow & \color{red}{750} x& = & 187 \\\Leftrightarrow & x = \frac{187}{750} & & \\ & V = \left\{ \frac{187}{750} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +10 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 10+132 \\\Leftrightarrow & \color{red}{385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{385} & & \\ & V = \left\{ \frac{142}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{4})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 28x-\frac{35}{4}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x- \frac{385}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{-385} & = & \color{red}{-220x} +16 \\\Leftrightarrow & 1232x \color{red}{-385} \color{blue}{+385} \color{blue}{+220x} & = & \color{red}{-220x} +16 \color{blue}{+220x} \color{blue}{+385} \\\Leftrightarrow & 1232x+220x& = & 16+385 \\\Leftrightarrow & \color{red}{1452} x& = & 401 \\\Leftrightarrow & x = \frac{401}{1452} & & \\ & V = \left\{ \frac{401}{1452} \right\} & \\\end{align}\)