Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 30x-\frac{18}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x- \frac{18}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{-18} & = & \color{red}{-49x} +9 \\\Leftrightarrow & 210x \color{red}{-18} \color{blue}{+18} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+18} \\\Leftrightarrow & 210x+49x& = & 9+18 \\\Leftrightarrow & \color{red}{259} x& = & 27 \\\Leftrightarrow & x = \frac{27}{259} & & \\ & V = \left\{ \frac{27}{259} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x-\frac{8}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{32}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-32} & = & \color{red}{-196x} +21 \\\Leftrightarrow & -168x \color{red}{-32} \color{blue}{+32} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{+32} \\\Leftrightarrow & -168x+196x& = & 21+32 \\\Leftrightarrow & \color{red}{28} x& = & 53 \\\Leftrightarrow & x = \frac{53}{28} & & \\ & V = \left\{ \frac{53}{28} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -120x+135x& = & 10+36 \\\Leftrightarrow & \color{red}{15} x& = & 46 \\\Leftrightarrow & x = \frac{46}{15} & & \\ & V = \left\{ \frac{46}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{5})& = & -4x+\frac{7}{11} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{-308} & = & \color{red}{-220x} +35 \\\Leftrightarrow & 1155x \color{red}{-308} \color{blue}{+308} \color{blue}{+220x} & = & \color{red}{-220x} +35 \color{blue}{+220x} \color{blue}{+308} \\\Leftrightarrow & 1155x+220x& = & 35+308 \\\Leftrightarrow & \color{red}{1375} x& = & 343 \\\Leftrightarrow & x = \frac{343}{1375} & & \\ & V = \left\{ \frac{343}{1375} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{11})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -14x+\frac{21}{11}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+21} & = & \color{red}{-33x} +8 \\\Leftrightarrow & -154x \color{red}{+21} \color{blue}{-21} \color{blue}{+33x} & = & \color{red}{-33x} +8 \color{blue}{+33x} \color{blue}{-21} \\\Leftrightarrow & -154x+33x& = & 8-21 \\\Leftrightarrow & \color{red}{-121} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-121} & & \\\Leftrightarrow & x = \frac{13}{121} & & \\ & V = \left\{ \frac{13}{121} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{12})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 28x+\frac{35}{12}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1680}{ \color{blue}{60} }x+ \frac{175}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{18}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1680x \color{red}{+175} & = & \color{red}{-300x} +18 \\\Leftrightarrow & 1680x \color{red}{+175} \color{blue}{-175} \color{blue}{+300x} & = & \color{red}{-300x} +18 \color{blue}{+300x} \color{blue}{-175} \\\Leftrightarrow & 1680x+300x& = & 18-175 \\\Leftrightarrow & \color{red}{1980} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{1980} & & \\ & V = \left\{ \frac{-157}{1980} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{9})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -35x-\frac{35}{9}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-35} & = & \color{red}{-81x} +2 \\\Leftrightarrow & -315x \color{red}{-35} \color{blue}{+35} \color{blue}{+81x} & = & \color{red}{-81x} +2 \color{blue}{+81x} \color{blue}{+35} \\\Leftrightarrow & -315x+81x& = & 2+35 \\\Leftrightarrow & \color{red}{-234} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-234} & & \\\Leftrightarrow & x = \frac{-37}{234} & & \\ & V = \left\{ \frac{-37}{234} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{-15} & = & \color{red}{-28x} +7 \\\Leftrightarrow & -80x \color{red}{-15} \color{blue}{+15} \color{blue}{+28x} & = & \color{red}{-28x} +7 \color{blue}{+28x} \color{blue}{+15} \\\Leftrightarrow & -80x+28x& = & 7+15 \\\Leftrightarrow & \color{red}{-52} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-52} & & \\\Leftrightarrow & x = \frac{-11}{26} & & \\ & V = \left\{ \frac{-11}{26} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{385x} +40 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 660x-385x& = & 40-132 \\\Leftrightarrow & \color{red}{275} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{275} & & \\ & V = \left\{ \frac{-92}{275} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{11})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 28x+\frac{14}{11}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x+ \frac{70}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{+70} & = & \color{red}{165x} +44 \\\Leftrightarrow & 1540x \color{red}{+70} \color{blue}{-70} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-70} \\\Leftrightarrow & 1540x-165x& = & 44-70 \\\Leftrightarrow & \color{red}{1375} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{1375} & & \\ & V = \left\{ \frac{-26}{1375} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -28x+\frac{28}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x+ \frac{56}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{+56} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -616x \color{red}{+56} \color{blue}{-56} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-56} \\\Leftrightarrow & -616x+110x& = & 33-56 \\\Leftrightarrow & \color{red}{-506} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-506} & & \\\Leftrightarrow & x = \frac{1}{22} & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{385x} +40 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1650x-385x& = & 40-132 \\\Leftrightarrow & \color{red}{1265} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{1265} & & \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)