Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 14x-\frac{28}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{154}{ \color{blue}{11} }x- \frac{28}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 154x \color{red}{-28} & = & \color{red}{-55x} +10 \\\Leftrightarrow & 154x \color{red}{-28} \color{blue}{+28} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{+28} \\\Leftrightarrow & 154x+55x& = & 10+28 \\\Leftrightarrow & \color{red}{209} x& = & 38 \\\Leftrightarrow & x = \frac{38}{209} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+44} & = & \color{red}{297x} +12 \\\Leftrightarrow & -132x \color{red}{+44} \color{blue}{-44} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{-44} \\\Leftrightarrow & -132x-297x& = & 12-44 \\\Leftrightarrow & \color{red}{-429} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-429} & & \\\Leftrightarrow & x = \frac{32}{429} & & \\ & V = \left\{ \frac{32}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{5})& = & -9x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{16}{5}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{112}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-112} & = & \color{red}{-315x} +10 \\\Leftrightarrow & 280x \color{red}{-112} \color{blue}{+112} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{+112} \\\Leftrightarrow & 280x+315x& = & 10+112 \\\Leftrightarrow & \color{red}{595} x& = & 122 \\\Leftrightarrow & x = \frac{122}{595} & & \\ & V = \left\{ \frac{122}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{4})& = & -3x+\frac{7}{12} \\\Leftrightarrow & -28x-\frac{21}{4}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x- \frac{63}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{-63} & = & \color{red}{-36x} +7 \\\Leftrightarrow & -336x \color{red}{-63} \color{blue}{+63} \color{blue}{+36x} & = & \color{red}{-36x} +7 \color{blue}{+36x} \color{blue}{+63} \\\Leftrightarrow & -336x+36x& = & 7+63 \\\Leftrightarrow & \color{red}{-300} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-300} & & \\\Leftrightarrow & x = \frac{-7}{30} & & \\ & V = \left\{ \frac{-7}{30} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & -4x+\frac{9}{2} \\\Leftrightarrow & 21x+\frac{21}{11}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x+ \frac{42}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{+42} & = & \color{red}{-88x} +99 \\\Leftrightarrow & 462x \color{red}{+42} \color{blue}{-42} \color{blue}{+88x} & = & \color{red}{-88x} +99 \color{blue}{+88x} \color{blue}{-42} \\\Leftrightarrow & 462x+88x& = & 99-42 \\\Leftrightarrow & \color{red}{550} x& = & 57 \\\Leftrightarrow & x = \frac{57}{550} & & \\ & V = \left\{ \frac{57}{550} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & -9x+\frac{7}{9} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+90} & = & \color{red}{-567x} +49 \\\Leftrightarrow & -1575x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +49 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & -1575x+567x& = & 49-90 \\\Leftrightarrow & \color{red}{-1008} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-1008} & & \\\Leftrightarrow & x = \frac{41}{1008} & & \\ & V = \left\{ \frac{41}{1008} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+196} & = & \color{red}{70x} +50 \\\Leftrightarrow & 735x \color{red}{+196} \color{blue}{-196} \color{blue}{-70x} & = & \color{red}{70x} +50 \color{blue}{-70x} \color{blue}{-196} \\\Leftrightarrow & 735x-70x& = & 50-196 \\\Leftrightarrow & \color{red}{665} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{665} & & \\ & V = \left\{ \frac{-146}{665} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+64} & = & \color{red}{140x} +21 \\\Leftrightarrow & -336x \color{red}{+64} \color{blue}{-64} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-64} \\\Leftrightarrow & -336x-140x& = & 21-64 \\\Leftrightarrow & \color{red}{-476} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-476} & & \\\Leftrightarrow & x = \frac{43}{476} & & \\ & V = \left\{ \frac{43}{476} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{2})& = & 4x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{15}{2}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{72}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+135} & = & \color{red}{72x} +4 \\\Leftrightarrow & 270x \color{red}{+135} \color{blue}{-135} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{-135} \\\Leftrightarrow & 270x-72x& = & 4-135 \\\Leftrightarrow & \color{red}{198} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{198} & & \\ & V = \left\{ \frac{-131}{198} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & 210x+147x& = & 14-30 \\\Leftrightarrow & \color{red}{357} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{357} & & \\ & V = \left\{ \frac{-16}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-140} & = & \color{red}{-120x} +18 \\\Leftrightarrow & -315x \color{red}{-140} \color{blue}{+140} \color{blue}{+120x} & = & \color{red}{-120x} +18 \color{blue}{+120x} \color{blue}{+140} \\\Leftrightarrow & -315x+120x& = & 18+140 \\\Leftrightarrow & \color{red}{-195} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-195} & & \\\Leftrightarrow & x = \frac{-158}{195} & & \\ & V = \left\{ \frac{-158}{195} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & -2x+\frac{7}{2} \\\Leftrightarrow & 21x+\frac{28}{9}& = & -2x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{378}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{-36}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 378x \color{red}{+56} & = & \color{red}{-36x} +63 \\\Leftrightarrow & 378x \color{red}{+56} \color{blue}{-56} \color{blue}{+36x} & = & \color{red}{-36x} +63 \color{blue}{+36x} \color{blue}{-56} \\\Leftrightarrow & 378x+36x& = & 63-56 \\\Leftrightarrow & \color{red}{414} x& = & 7 \\\Leftrightarrow & x = \frac{7}{414} & & \\ & V = \left\{ \frac{7}{414} \right\} & \\\end{align}\)