Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{3})& = & 4x+\frac{3}{11} \\\Leftrightarrow & -15x-\frac{20}{3}& = & 4x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-220} & = & \color{red}{132x} +9 \\\Leftrightarrow & -495x \color{red}{-220} \color{blue}{+220} \color{blue}{-132x} & = & \color{red}{132x} +9 \color{blue}{-132x} \color{blue}{+220} \\\Leftrightarrow & -495x-132x& = & 9+220 \\\Leftrightarrow & \color{red}{-627} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-627} & & \\\Leftrightarrow & x = \frac{-229}{627} & & \\ & V = \left\{ \frac{-229}{627} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & 2x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{9}{5}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+99} & = & \color{red}{110x} +50 \\\Leftrightarrow & 825x \color{red}{+99} \color{blue}{-99} \color{blue}{-110x} & = & \color{red}{110x} +50 \color{blue}{-110x} \color{blue}{-99} \\\Leftrightarrow & 825x-110x& = & 50-99 \\\Leftrightarrow & \color{red}{715} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{715} & & \\ & V = \left\{ \frac{-49}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 28x+\frac{28}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{27x} +12 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{-28} \\\Leftrightarrow & 252x-27x& = & 12-28 \\\Leftrightarrow & \color{red}{225} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{225} & & \\ & V = \left\{ \frac{-16}{225} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{9})& = & -2x+\frac{5}{8} \\\Leftrightarrow & 21x-\frac{14}{9}& = & -2x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1512}{ \color{blue}{72} }x- \frac{112}{ \color{blue}{72} })& = & (\frac{-144}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1512x \color{red}{-112} & = & \color{red}{-144x} +45 \\\Leftrightarrow & 1512x \color{red}{-112} \color{blue}{+112} \color{blue}{+144x} & = & \color{red}{-144x} +45 \color{blue}{+144x} \color{blue}{+112} \\\Leftrightarrow & 1512x+144x& = & 45+112 \\\Leftrightarrow & \color{red}{1656} x& = & 157 \\\Leftrightarrow & x = \frac{157}{1656} & & \\ & V = \left\{ \frac{157}{1656} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{21}{10}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+21} & = & \color{red}{-50x} +12 \\\Leftrightarrow & 210x \color{red}{+21} \color{blue}{-21} \color{blue}{+50x} & = & \color{red}{-50x} +12 \color{blue}{+50x} \color{blue}{-21} \\\Leftrightarrow & 210x+50x& = & 12-21 \\\Leftrightarrow & \color{red}{260} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{260} & & \\ & V = \left\{ \frac{-9}{260} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{8})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{15}{8}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{432}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 432x \color{red}{+135} & = & \color{red}{-360x} +32 \\\Leftrightarrow & 432x \color{red}{+135} \color{blue}{-135} \color{blue}{+360x} & = & \color{red}{-360x} +32 \color{blue}{+360x} \color{blue}{-135} \\\Leftrightarrow & 432x+360x& = & 32-135 \\\Leftrightarrow & \color{red}{792} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{792} & & \\ & V = \left\{ \frac{-103}{792} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -3x+\frac{9}{5} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+80} & = & \color{red}{-105x} +63 \\\Leftrightarrow & -700x \color{red}{+80} \color{blue}{-80} \color{blue}{+105x} & = & \color{red}{-105x} +63 \color{blue}{+105x} \color{blue}{-80} \\\Leftrightarrow & -700x+105x& = & 63-80 \\\Leftrightarrow & \color{red}{-595} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-595} & & \\\Leftrightarrow & x = \frac{1}{35} & & \\ & V = \left\{ \frac{1}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{6})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{25}{6}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-420}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -420x \color{red}{-175} & = & \color{red}{-294x} +54 \\\Leftrightarrow & -420x \color{red}{-175} \color{blue}{+175} \color{blue}{+294x} & = & \color{red}{-294x} +54 \color{blue}{+294x} \color{blue}{+175} \\\Leftrightarrow & -420x+294x& = & 54+175 \\\Leftrightarrow & \color{red}{-126} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-126} & & \\\Leftrightarrow & x = \frac{-229}{126} & & \\ & V = \left\{ \frac{-229}{126} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+50} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -280x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & -280x+315x& = & 14-50 \\\Leftrightarrow & \color{red}{35} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{35} & & \\ & V = \left\{ \frac{-36}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{245x} +49 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & 350x-245x& = & 49+50 \\\Leftrightarrow & \color{red}{105} x& = & 99 \\\Leftrightarrow & x = \frac{99}{105} & & \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-28} & = & \color{red}{441x} +81 \\\Leftrightarrow & -378x \color{red}{-28} \color{blue}{+28} \color{blue}{-441x} & = & \color{red}{441x} +81 \color{blue}{-441x} \color{blue}{+28} \\\Leftrightarrow & -378x-441x& = & 81+28 \\\Leftrightarrow & \color{red}{-819} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-819} & & \\\Leftrightarrow & x = \frac{-109}{819} & & \\ & V = \left\{ \frac{-109}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+45} & = & \color{red}{24x} +16 \\\Leftrightarrow & 300x \color{red}{+45} \color{blue}{-45} \color{blue}{-24x} & = & \color{red}{24x} +16 \color{blue}{-24x} \color{blue}{-45} \\\Leftrightarrow & 300x-24x& = & 16-45 \\\Leftrightarrow & \color{red}{276} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{276} & & \\ & V = \left\{ \frac{-29}{276} \right\} & \\\end{align}\)