Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+14} & = & \color{red}{9x} +10 \\\Leftrightarrow & -42x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +10 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & -42x-9x& = & 10-14 \\\Leftrightarrow & \color{red}{-51} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-51} & & \\\Leftrightarrow & x = \frac{4}{51} & & \\ & V = \left\{ \frac{4}{51} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -90x+105x& = & 50-18 \\\Leftrightarrow & \color{red}{15} x& = & 32 \\\Leftrightarrow & x = \frac{32}{15} & & \\ & V = \left\{ \frac{32}{15} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{231x} +88 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & 330x-231x& = & 88+30 \\\Leftrightarrow & \color{red}{99} x& = & 118 \\\Leftrightarrow & x = \frac{118}{99} & & \\ & V = \left\{ \frac{118}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 14x+\frac{28}{3}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+308} & = & \color{red}{99x} +24 \\\Leftrightarrow & 462x \color{red}{+308} \color{blue}{-308} \color{blue}{-99x} & = & \color{red}{99x} +24 \color{blue}{-99x} \color{blue}{-308} \\\Leftrightarrow & 462x-99x& = & 24-308 \\\Leftrightarrow & \color{red}{363} x& = & -284 \\\Leftrightarrow & x = \frac{-284}{363} & & \\ & V = \left\{ \frac{-284}{363} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{-112x} +40 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +40 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & 252x+112x& = & 40+105 \\\Leftrightarrow & \color{red}{364} x& = & 145 \\\Leftrightarrow & x = \frac{145}{364} & & \\ & V = \left\{ \frac{145}{364} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+54} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 378x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & 378x+315x& = & 14-54 \\\Leftrightarrow & \color{red}{693} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{693} & & \\ & V = \left\{ \frac{-40}{693} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{36}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{100x} +45 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+36} \\\Leftrightarrow & -180x-100x& = & 45+36 \\\Leftrightarrow & \color{red}{-280} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-280} & & \\\Leftrightarrow & x = \frac{-81}{280} & & \\ & V = \left\{ \frac{-81}{280} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 30x-\frac{24}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{-24} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 210x \color{red}{-24} \color{blue}{+24} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+24} \\\Leftrightarrow & 210x+49x& = & 10+24 \\\Leftrightarrow & \color{red}{259} x& = & 34 \\\Leftrightarrow & x = \frac{34}{259} & & \\ & V = \left\{ \frac{34}{259} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{9})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-44} & = & \color{red}{495x} +27 \\\Leftrightarrow & 792x \color{red}{-44} \color{blue}{+44} \color{blue}{-495x} & = & \color{red}{495x} +27 \color{blue}{-495x} \color{blue}{+44} \\\Leftrightarrow & 792x-495x& = & 27+44 \\\Leftrightarrow & \color{red}{297} x& = & 71 \\\Leftrightarrow & x = \frac{71}{297} & & \\ & V = \left\{ \frac{71}{297} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{6}{5}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{600}{ \color{blue}{60} }x- \frac{72}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 600x \color{red}{-72} & = & \color{red}{-180x} +25 \\\Leftrightarrow & 600x \color{red}{-72} \color{blue}{+72} \color{blue}{+180x} & = & \color{red}{-180x} +25 \color{blue}{+180x} \color{blue}{+72} \\\Leftrightarrow & 600x+180x& = & 25+72 \\\Leftrightarrow & \color{red}{780} x& = & 97 \\\Leftrightarrow & x = \frac{97}{780} & & \\ & V = \left\{ \frac{97}{780} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{6})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{35}{6}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{-175} & = & \color{red}{-270x} +36 \\\Leftrightarrow & -1050x \color{red}{-175} \color{blue}{+175} \color{blue}{+270x} & = & \color{red}{-270x} +36 \color{blue}{+270x} \color{blue}{+175} \\\Leftrightarrow & -1050x+270x& = & 36+175 \\\Leftrightarrow & \color{red}{-780} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-780} & & \\\Leftrightarrow & x = \frac{-211}{780} & & \\ & V = \left\{ \frac{-211}{780} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{9})& = & 8x+\frac{2}{9} \\\Leftrightarrow & 25x+\frac{10}{9}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+10} & = & \color{red}{72x} +2 \\\Leftrightarrow & 225x \color{red}{+10} \color{blue}{-10} \color{blue}{-72x} & = & \color{red}{72x} +2 \color{blue}{-72x} \color{blue}{-10} \\\Leftrightarrow & 225x-72x& = & 2-10 \\\Leftrightarrow & \color{red}{153} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{153} & & \\ & V = \left\{ \frac{-8}{153} \right\} & \\\end{align}\)