Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{-99x} +30 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+99x} & = & \color{red}{-99x} +30 \color{blue}{+99x} \color{blue}{+154} \\\Leftrightarrow & -1155x+99x& = & 30+154 \\\Leftrightarrow & \color{red}{-1056} x& = & 184 \\\Leftrightarrow & x = \frac{184}{-1056} & & \\\Leftrightarrow & x = \frac{-23}{132} & & \\ & V = \left\{ \frac{-23}{132} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -6x-\frac{15}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-135} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -378x \color{red}{-135} \color{blue}{+135} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{+135} \\\Leftrightarrow & -378x+441x& = & 49+135 \\\Leftrightarrow & \color{red}{63} x& = & 184 \\\Leftrightarrow & x = \frac{184}{63} & & \\ & V = \left\{ \frac{184}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+44} & = & \color{red}{-385x} +50 \\\Leftrightarrow & -550x \color{red}{+44} \color{blue}{-44} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-44} \\\Leftrightarrow & -550x+385x& = & 50-44 \\\Leftrightarrow & \color{red}{-165} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-165} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 330x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 330x+275x& = & 10-132 \\\Leftrightarrow & \color{red}{605} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{605} & & \\ & V = \left\{ \frac{-122}{605} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -6x+\frac{4}{9} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -6x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{-54x} +4 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{-42} \\\Leftrightarrow & 315x+54x& = & 4-42 \\\Leftrightarrow & \color{red}{369} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{369} & & \\ & V = \left\{ \frac{-38}{369} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-100} & = & \color{red}{315x} +54 \\\Leftrightarrow & 900x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & 900x-315x& = & 54+100 \\\Leftrightarrow & \color{red}{585} x& = & 154 \\\Leftrightarrow & x = \frac{154}{585} & & \\ & V = \left\{ \frac{154}{585} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{9})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 35x-\frac{28}{9}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-308} & = & \color{red}{198x} +18 \\\Leftrightarrow & 3465x \color{red}{-308} \color{blue}{+308} \color{blue}{-198x} & = & \color{red}{198x} +18 \color{blue}{-198x} \color{blue}{+308} \\\Leftrightarrow & 3465x-198x& = & 18+308 \\\Leftrightarrow & \color{red}{3267} x& = & 326 \\\Leftrightarrow & x = \frac{326}{3267} & & \\ & V = \left\{ \frac{326}{3267} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -770x-539x& = & 70-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1309} & & \\\Leftrightarrow & x = \frac{40}{1309} & & \\ & V = \left\{ \frac{40}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-12} \\\Leftrightarrow & 84x+49x& = & 10-12 \\\Leftrightarrow & \color{red}{133} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{133} & & \\ & V = \left\{ \frac{-2}{133} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{-25x} +7 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+25x} & = & \color{red}{-25x} +7 \color{blue}{+25x} \color{blue}{-6} \\\Leftrightarrow & 30x+25x& = & 7-6 \\\Leftrightarrow & \color{red}{55} x& = & 1 \\\Leftrightarrow & x = \frac{1}{55} & & \\ & V = \left\{ \frac{1}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{3})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 25x-\frac{10}{3}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{-20} & = & \color{red}{54x} +15 \\\Leftrightarrow & 150x \color{red}{-20} \color{blue}{+20} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{+20} \\\Leftrightarrow & 150x-54x& = & 15+20 \\\Leftrightarrow & \color{red}{96} x& = & 35 \\\Leftrightarrow & x = \frac{35}{96} & & \\ & V = \left\{ \frac{35}{96} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & 300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 300x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{230} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{230} & & \\ & V = \left\{ \frac{-9}{230} \right\} & \\\end{align}\)