Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{25}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-25} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 220x \color{red}{-25} \color{blue}{+25} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+25} \\\Leftrightarrow & 220x+99x& = & 6+25 \\\Leftrightarrow & \color{red}{319} x& = & 31 \\\Leftrightarrow & x = \frac{31}{319} & & \\ & V = \left\{ \frac{31}{319} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{5})& = & 3x+\frac{9}{5} \\\Leftrightarrow & -35x+\frac{28}{5}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x+ \frac{28}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{+28} & = & \color{red}{15x} +9 \\\Leftrightarrow & -175x \color{red}{+28} \color{blue}{-28} \color{blue}{-15x} & = & \color{red}{15x} +9 \color{blue}{-15x} \color{blue}{-28} \\\Leftrightarrow & -175x-15x& = & 9-28 \\\Leftrightarrow & \color{red}{-190} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-190} & & \\\Leftrightarrow & x = \frac{1}{10} & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+77} & = & \color{red}{-297x} +30 \\\Leftrightarrow & 1155x \color{red}{+77} \color{blue}{-77} \color{blue}{+297x} & = & \color{red}{-297x} +30 \color{blue}{+297x} \color{blue}{-77} \\\Leftrightarrow & 1155x+297x& = & 30-77 \\\Leftrightarrow & \color{red}{1452} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{1452} & & \\ & V = \left\{ \frac{-47}{1452} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 9x-\frac{6}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-6} & = & \color{red}{77x} +5 \\\Leftrightarrow & 99x \color{red}{-6} \color{blue}{+6} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+6} \\\Leftrightarrow & 99x-77x& = & 5+6 \\\Leftrightarrow & \color{red}{22} x& = & 11 \\\Leftrightarrow & x = \frac{11}{22} & & \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{2})& = & -4x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{25}{2}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{100}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-100} & = & \color{red}{-32x} +7 \\\Leftrightarrow & 120x \color{red}{-100} \color{blue}{+100} \color{blue}{+32x} & = & \color{red}{-32x} +7 \color{blue}{+32x} \color{blue}{+100} \\\Leftrightarrow & 120x+32x& = & 7+100 \\\Leftrightarrow & \color{red}{152} x& = & 107 \\\Leftrightarrow & x = \frac{107}{152} & & \\ & V = \left\{ \frac{107}{152} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{70x} +45 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -300x-70x& = & 45-24 \\\Leftrightarrow & \color{red}{-370} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-370} & & \\\Leftrightarrow & x = \frac{-21}{370} & & \\ & V = \left\{ \frac{-21}{370} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{3})& = & 4x+\frac{6}{7} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 4x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+98} & = & \color{red}{84x} +18 \\\Leftrightarrow & -735x \color{red}{+98} \color{blue}{-98} \color{blue}{-84x} & = & \color{red}{84x} +18 \color{blue}{-84x} \color{blue}{-98} \\\Leftrightarrow & -735x-84x& = & 18-98 \\\Leftrightarrow & \color{red}{-819} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{-819} & & \\\Leftrightarrow & x = \frac{80}{819} & & \\ & V = \left\{ \frac{80}{819} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{3})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{28}{3}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{-140} & = & \color{red}{-135x} +24 \\\Leftrightarrow & 210x \color{red}{-140} \color{blue}{+140} \color{blue}{+135x} & = & \color{red}{-135x} +24 \color{blue}{+135x} \color{blue}{+140} \\\Leftrightarrow & 210x+135x& = & 24+140 \\\Leftrightarrow & \color{red}{345} x& = & 164 \\\Leftrightarrow & x = \frac{164}{345} & & \\ & V = \left\{ \frac{164}{345} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{6})& = & -4x+\frac{5}{7} \\\Leftrightarrow & 15x+\frac{25}{6}& = & -4x+\frac{5}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{-168}{ \color{blue}{42} }x+ \frac{30}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+175} & = & \color{red}{-168x} +30 \\\Leftrightarrow & 630x \color{red}{+175} \color{blue}{-175} \color{blue}{+168x} & = & \color{red}{-168x} +30 \color{blue}{+168x} \color{blue}{-175} \\\Leftrightarrow & 630x+168x& = & 30-175 \\\Leftrightarrow & \color{red}{798} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{798} & & \\ & V = \left\{ \frac{-145}{798} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{18}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{70x} +15 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-36} \\\Leftrightarrow & 300x-70x& = & 15-36 \\\Leftrightarrow & \color{red}{230} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{230} & & \\ & V = \left\{ \frac{-21}{230} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -16x-\frac{8}{9}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-40} & = & \color{red}{315x} +81 \\\Leftrightarrow & -720x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +81 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -720x-315x& = & 81+40 \\\Leftrightarrow & \color{red}{-1035} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-1035} & & \\\Leftrightarrow & x = \frac{-121}{1035} & & \\ & V = \left\{ \frac{-121}{1035} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+18} & = & \color{red}{-55x} +10 \\\Leftrightarrow & 264x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & 264x+55x& = & 10-18 \\\Leftrightarrow & \color{red}{319} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{319} & & \\ & V = \left\{ \frac{-8}{319} \right\} & \\\end{align}\)