Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-196} & = & \color{red}{567x} +72 \\\Leftrightarrow & 882x \color{red}{-196} \color{blue}{+196} \color{blue}{-567x} & = & \color{red}{567x} +72 \color{blue}{-567x} \color{blue}{+196} \\\Leftrightarrow & 882x-567x& = & 72+196 \\\Leftrightarrow & \color{red}{315} x& = & 268 \\\Leftrightarrow & x = \frac{268}{315} & & \\ & V = \left\{ \frac{268}{315} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+24} & = & \color{red}{231x} +88 \\\Leftrightarrow & -198x \color{red}{+24} \color{blue}{-24} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-24} \\\Leftrightarrow & -198x-231x& = & 88-24 \\\Leftrightarrow & \color{red}{-429} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-429} & & \\\Leftrightarrow & x = \frac{-64}{429} & & \\ & V = \left\{ \frac{-64}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{3})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{25}{3}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x+ \frac{25}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{+25} & = & \color{red}{12x} +2 \\\Leftrightarrow & -45x \color{red}{+25} \color{blue}{-25} \color{blue}{-12x} & = & \color{red}{12x} +2 \color{blue}{-12x} \color{blue}{-25} \\\Leftrightarrow & -45x-12x& = & 2-25 \\\Leftrightarrow & \color{red}{-57} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-57} & & \\\Leftrightarrow & x = \frac{23}{57} & & \\ & V = \left\{ \frac{23}{57} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{5})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-8} & = & \color{red}{30x} +15 \\\Leftrightarrow & 80x \color{red}{-8} \color{blue}{+8} \color{blue}{-30x} & = & \color{red}{30x} +15 \color{blue}{-30x} \color{blue}{+8} \\\Leftrightarrow & 80x-30x& = & 15+8 \\\Leftrightarrow & \color{red}{50} x& = & 23 \\\Leftrightarrow & x = \frac{23}{50} & & \\ & V = \left\{ \frac{23}{50} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{35x} +10 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 126x-35x& = & 10-30 \\\Leftrightarrow & \color{red}{91} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{91} & & \\ & V = \left\{ \frac{-20}{91} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{5})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{16}{5}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{176}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+176} & = & \color{red}{-165x} +40 \\\Leftrightarrow & 1100x \color{red}{+176} \color{blue}{-176} \color{blue}{+165x} & = & \color{red}{-165x} +40 \color{blue}{+165x} \color{blue}{-176} \\\Leftrightarrow & 1100x+165x& = & 40-176 \\\Leftrightarrow & \color{red}{1265} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{1265} & & \\ & V = \left\{ \frac{-136}{1265} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 30x-\frac{24}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-72} & = & \color{red}{231x} +22 \\\Leftrightarrow & 990x \color{red}{-72} \color{blue}{+72} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+72} \\\Leftrightarrow & 990x-231x& = & 22+72 \\\Leftrightarrow & \color{red}{759} x& = & 94 \\\Leftrightarrow & x = \frac{94}{759} & & \\ & V = \left\{ \frac{94}{759} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{-27x} +2 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & 72x+27x& = & 2+8 \\\Leftrightarrow & \color{red}{99} x& = & 10 \\\Leftrightarrow & x = \frac{10}{99} & & \\ & V = \left\{ \frac{10}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-144} & = & \color{red}{441x} +14 \\\Leftrightarrow & 1008x \color{red}{-144} \color{blue}{+144} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{+144} \\\Leftrightarrow & 1008x-441x& = & 14+144 \\\Leftrightarrow & \color{red}{567} x& = & 158 \\\Leftrightarrow & x = \frac{158}{567} & & \\ & V = \left\{ \frac{158}{567} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{5})& = & -6x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{28}{5}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-308} & = & \color{red}{-330x} +30 \\\Leftrightarrow & -1925x \color{red}{-308} \color{blue}{+308} \color{blue}{+330x} & = & \color{red}{-330x} +30 \color{blue}{+330x} \color{blue}{+308} \\\Leftrightarrow & -1925x+330x& = & 30+308 \\\Leftrightarrow & \color{red}{-1595} x& = & 338 \\\Leftrightarrow & x = \frac{338}{-1595} & & \\\Leftrightarrow & x = \frac{-338}{1595} & & \\ & V = \left\{ \frac{-338}{1595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{-20} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 112x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & 112x+21x& = & 10+20 \\\Leftrightarrow & \color{red}{133} x& = & 30 \\\Leftrightarrow & x = \frac{30}{133} & & \\ & V = \left\{ \frac{30}{133} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{-200x} +64 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{+200x} & = & \color{red}{-200x} +64 \color{blue}{+200x} \color{blue}{-75} \\\Leftrightarrow & 480x+200x& = & 64-75 \\\Leftrightarrow & \color{red}{680} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{680} & & \\ & V = \left\{ \frac{-11}{680} \right\} & \\\end{align}\)