Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{8}{11}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{99x} +110 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{-99x} & = & \color{red}{99x} +110 \color{blue}{-99x} \color{blue}{-24} \\\Leftrightarrow & 132x-99x& = & 110-24 \\\Leftrightarrow & \color{red}{33} x& = & 86 \\\Leftrightarrow & x = \frac{86}{33} & & \\ & V = \left\{ \frac{86}{33} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{+24} \\\Leftrightarrow & 168x+140x& = & 21+24 \\\Leftrightarrow & \color{red}{308} x& = & 45 \\\Leftrightarrow & x = \frac{45}{308} & & \\ & V = \left\{ \frac{45}{308} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{6})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -15x+\frac{25}{6}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{12}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+125} & = & \color{red}{120x} +12 \\\Leftrightarrow & -450x \color{red}{+125} \color{blue}{-125} \color{blue}{-120x} & = & \color{red}{120x} +12 \color{blue}{-120x} \color{blue}{-125} \\\Leftrightarrow & -450x-120x& = & 12-125 \\\Leftrightarrow & \color{red}{-570} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-570} & & \\\Leftrightarrow & x = \frac{113}{570} & & \\ & V = \left\{ \frac{113}{570} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{7})& = & 4x+\frac{7}{12} \\\Leftrightarrow & 15x-\frac{25}{7}& = & 4x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1260}{ \color{blue}{84} }x- \frac{300}{ \color{blue}{84} })& = & (\frac{336}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1260x \color{red}{-300} & = & \color{red}{336x} +49 \\\Leftrightarrow & 1260x \color{red}{-300} \color{blue}{+300} \color{blue}{-336x} & = & \color{red}{336x} +49 \color{blue}{-336x} \color{blue}{+300} \\\Leftrightarrow & 1260x-336x& = & 49+300 \\\Leftrightarrow & \color{red}{924} x& = & 349 \\\Leftrightarrow & x = \frac{349}{924} & & \\ & V = \left\{ \frac{349}{924} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{3})& = & 9x+\frac{9}{11} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-385} & = & \color{red}{297x} +27 \\\Leftrightarrow & 1155x \color{red}{-385} \color{blue}{+385} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{+385} \\\Leftrightarrow & 1155x-297x& = & 27+385 \\\Leftrightarrow & \color{red}{858} x& = & 412 \\\Leftrightarrow & x = \frac{412}{858} & & \\\Leftrightarrow & x = \frac{206}{429} & & \\ & V = \left\{ \frac{206}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 4x+\frac{8}{7} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-98} & = & \color{red}{84x} +24 \\\Leftrightarrow & 441x \color{red}{-98} \color{blue}{+98} \color{blue}{-84x} & = & \color{red}{84x} +24 \color{blue}{-84x} \color{blue}{+98} \\\Leftrightarrow & 441x-84x& = & 24+98 \\\Leftrightarrow & \color{red}{357} x& = & 122 \\\Leftrightarrow & x = \frac{122}{357} & & \\ & V = \left\{ \frac{122}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 28x+\frac{35}{4}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{784}{ \color{blue}{28} }x+ \frac{245}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 784x \color{red}{+245} & = & \color{red}{-140x} +36 \\\Leftrightarrow & 784x \color{red}{+245} \color{blue}{-245} \color{blue}{+140x} & = & \color{red}{-140x} +36 \color{blue}{+140x} \color{blue}{-245} \\\Leftrightarrow & 784x+140x& = & 36-245 \\\Leftrightarrow & \color{red}{924} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{924} & & \\\Leftrightarrow & x = \frac{-19}{84} & & \\ & V = \left\{ \frac{-19}{84} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x- \frac{50}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{-50} & = & \color{red}{28x} +3 \\\Leftrightarrow & -80x \color{red}{-50} \color{blue}{+50} \color{blue}{-28x} & = & \color{red}{28x} +3 \color{blue}{-28x} \color{blue}{+50} \\\Leftrightarrow & -80x-28x& = & 3+50 \\\Leftrightarrow & \color{red}{-108} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-108} & & \\\Leftrightarrow & x = \frac{-53}{108} & & \\ & V = \left\{ \frac{-53}{108} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{+15} & = & \color{red}{28x} +6 \\\Leftrightarrow & -40x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +6 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & -40x-28x& = & 6-15 \\\Leftrightarrow & \color{red}{-68} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-68} & & \\\Leftrightarrow & x = \frac{9}{68} & & \\ & V = \left\{ \frac{9}{68} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & 6x+\frac{7}{2} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 6x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{36}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{36x} +21 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{-36x} & = & \color{red}{36x} +21 \color{blue}{-36x} \color{blue}{-28} \\\Leftrightarrow & -210x-36x& = & 21-28 \\\Leftrightarrow & \color{red}{-246} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-246} & & \\\Leftrightarrow & x = \frac{7}{246} & & \\ & V = \left\{ \frac{7}{246} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-18} & = & \color{red}{60x} +50 \\\Leftrightarrow & -225x \color{red}{-18} \color{blue}{+18} \color{blue}{-60x} & = & \color{red}{60x} +50 \color{blue}{-60x} \color{blue}{+18} \\\Leftrightarrow & -225x-60x& = & 50+18 \\\Leftrightarrow & \color{red}{-285} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-285} & & \\\Leftrightarrow & x = \frac{-68}{285} & & \\ & V = \left\{ \frac{-68}{285} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-10x} +9 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+10x} & = & \color{red}{-10x} +9 \color{blue}{+10x} \color{blue}{-12} \\\Leftrightarrow & 75x+10x& = & 9-12 \\\Leftrightarrow & \color{red}{85} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{85} & & \\ & V = \left\{ \frac{-3}{85} \right\} & \\\end{align}\)