Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 8x-\frac{4}{7}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{4}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-4} & = & \color{red}{21x} +9 \\\Leftrightarrow & 56x \color{red}{-4} \color{blue}{+4} \color{blue}{-21x} & = & \color{red}{21x} +9 \color{blue}{-21x} \color{blue}{+4} \\\Leftrightarrow & 56x-21x& = & 9+4 \\\Leftrightarrow & \color{red}{35} x& = & 13 \\\Leftrightarrow & x = \frac{13}{35} & & \\ & V = \left\{ \frac{13}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-196x} +49 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+196x} & = & \color{red}{-196x} +49 \color{blue}{+196x} \color{blue}{+40} \\\Leftrightarrow & -280x+196x& = & 49+40 \\\Leftrightarrow & \color{red}{-84} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-84} & & \\\Leftrightarrow & x = \frac{-89}{84} & & \\ & V = \left\{ \frac{-89}{84} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-96} & = & \color{red}{280x} +35 \\\Leftrightarrow & 1200x \color{red}{-96} \color{blue}{+96} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+96} \\\Leftrightarrow & 1200x-280x& = & 35+96 \\\Leftrightarrow & \color{red}{920} x& = & 131 \\\Leftrightarrow & x = \frac{131}{920} & & \\ & V = \left\{ \frac{131}{920} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-112x} +16 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+112x} & = & \color{red}{-112x} +16 \color{blue}{+112x} \color{blue}{-105} \\\Leftrightarrow & -420x+112x& = & 16-105 \\\Leftrightarrow & \color{red}{-308} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-308} & & \\\Leftrightarrow & x = \frac{89}{308} & & \\ & V = \left\{ \frac{89}{308} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{+75} & = & \color{red}{100x} +32 \\\Leftrightarrow & -180x \color{red}{+75} \color{blue}{-75} \color{blue}{-100x} & = & \color{red}{100x} +32 \color{blue}{-100x} \color{blue}{-75} \\\Leftrightarrow & -180x-100x& = & 32-75 \\\Leftrightarrow & \color{red}{-280} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-280} & & \\\Leftrightarrow & x = \frac{43}{280} & & \\ & V = \left\{ \frac{43}{280} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & 792x+231x& = & 110+54 \\\Leftrightarrow & \color{red}{1023} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1023} & & \\ & V = \left\{ \frac{164}{1023} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{60x} +25 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{+72} \\\Leftrightarrow & 270x-60x& = & 25+72 \\\Leftrightarrow & \color{red}{210} x& = & 97 \\\Leftrightarrow & x = \frac{97}{210} & & \\ & V = \left\{ \frac{97}{210} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-18} & = & \color{red}{25x} +6 \\\Leftrightarrow & -120x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & -120x-25x& = & 6+18 \\\Leftrightarrow & \color{red}{-145} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-145} & & \\\Leftrightarrow & x = \frac{-24}{145} & & \\ & V = \left\{ \frac{-24}{145} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{15}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+15} & = & \color{red}{77x} +4 \\\Leftrightarrow & 165x \color{red}{+15} \color{blue}{-15} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-15} \\\Leftrightarrow & 165x-77x& = & 4-15 \\\Leftrightarrow & \color{red}{88} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{88} & & \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & 6x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{21}{4}& = & 6x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{63}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-63} & = & \color{red}{72x} +8 \\\Leftrightarrow & 420x \color{red}{-63} \color{blue}{+63} \color{blue}{-72x} & = & \color{red}{72x} +8 \color{blue}{-72x} \color{blue}{+63} \\\Leftrightarrow & 420x-72x& = & 8+63 \\\Leftrightarrow & \color{red}{348} x& = & 71 \\\Leftrightarrow & x = \frac{71}{348} & & \\ & V = \left\{ \frac{71}{348} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{4}{3}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-28} & = & \color{red}{63x} +30 \\\Leftrightarrow & 168x \color{red}{-28} \color{blue}{+28} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+28} \\\Leftrightarrow & 168x-63x& = & 30+28 \\\Leftrightarrow & \color{red}{105} x& = & 58 \\\Leftrightarrow & x = \frac{58}{105} & & \\ & V = \left\{ \frac{58}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{189x} +56 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-18} \\\Leftrightarrow & -84x-189x& = & 56-18 \\\Leftrightarrow & \color{red}{-273} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-273} & & \\\Leftrightarrow & x = \frac{-38}{273} & & \\ & V = \left\{ \frac{-38}{273} \right\} & \\\end{align}\)