Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{2})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{9}{2}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-12}{ \color{blue}{2} }x- \frac{9}{ \color{blue}{2} })& = & (\frac{14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -12x \color{red}{-9} & = & \color{red}{14x} +3 \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{-14x} & = & \color{red}{14x} +3 \color{blue}{-14x} \color{blue}{+9} \\\Leftrightarrow & -12x-14x& = & 3+9 \\\Leftrightarrow & \color{red}{-26} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-26} & & \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+35} & = & \color{red}{-30x} +4 \\\Leftrightarrow & 84x \color{red}{+35} \color{blue}{-35} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{-35} \\\Leftrightarrow & 84x+30x& = & 4-35 \\\Leftrightarrow & \color{red}{114} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{114} & & \\ & V = \left\{ \frac{-31}{114} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{4}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+20} & = & \color{red}{105x} +18 \\\Leftrightarrow & 90x \color{red}{+20} \color{blue}{-20} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-20} \\\Leftrightarrow & 90x-105x& = & 18-20 \\\Leftrightarrow & \color{red}{-15} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-15} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{11})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+72} & = & \color{red}{891x} +88 \\\Leftrightarrow & 1980x \color{red}{+72} \color{blue}{-72} \color{blue}{-891x} & = & \color{red}{891x} +88 \color{blue}{-891x} \color{blue}{-72} \\\Leftrightarrow & 1980x-891x& = & 88-72 \\\Leftrightarrow & \color{red}{1089} x& = & 16 \\\Leftrightarrow & x = \frac{16}{1089} & & \\ & V = \left\{ \frac{16}{1089} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 30-132 \\\Leftrightarrow & \color{red}{-935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-935} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{147x} +35 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 126x-147x& = & 35+18 \\\Leftrightarrow & \color{red}{-21} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-21} & & \\\Leftrightarrow & x = \frac{-53}{21} & & \\ & V = \left\{ \frac{-53}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -30x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{-65} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-65} & & \\\Leftrightarrow & x = \frac{6}{65} & & \\ & V = \left\{ \frac{6}{65} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-140} & = & \color{red}{-84x} +30 \\\Leftrightarrow & 315x \color{red}{-140} \color{blue}{+140} \color{blue}{+84x} & = & \color{red}{-84x} +30 \color{blue}{+84x} \color{blue}{+140} \\\Leftrightarrow & 315x+84x& = & 30+140 \\\Leftrightarrow & \color{red}{399} x& = & 170 \\\Leftrightarrow & x = \frac{170}{399} & & \\ & V = \left\{ \frac{170}{399} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{21x} +10 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & 140x-21x& = & 10-20 \\\Leftrightarrow & \color{red}{119} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{119} & & \\ & V = \left\{ \frac{-10}{119} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{6})& = & 6x+\frac{7}{10} \\\Leftrightarrow & -25x-\frac{25}{6}& = & 6x+\frac{7}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-750}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{180}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -750x \color{red}{-125} & = & \color{red}{180x} +21 \\\Leftrightarrow & -750x \color{red}{-125} \color{blue}{+125} \color{blue}{-180x} & = & \color{red}{180x} +21 \color{blue}{-180x} \color{blue}{+125} \\\Leftrightarrow & -750x-180x& = & 21+125 \\\Leftrightarrow & \color{red}{-930} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-930} & & \\\Leftrightarrow & x = \frac{-73}{465} & & \\ & V = \left\{ \frac{-73}{465} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{120x} +25 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{-120x} & = & \color{red}{120x} +25 \color{blue}{-120x} \color{blue}{-72} \\\Leftrightarrow & -450x-120x& = & 25-72 \\\Leftrightarrow & \color{red}{-570} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-570} & & \\\Leftrightarrow & x = \frac{47}{570} & & \\ & V = \left\{ \frac{47}{570} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{36}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{-15} & = & \color{red}{36x} +14 \\\Leftrightarrow & 40x \color{red}{-15} \color{blue}{+15} \color{blue}{-36x} & = & \color{red}{36x} +14 \color{blue}{-36x} \color{blue}{+15} \\\Leftrightarrow & 40x-36x& = & 14+15 \\\Leftrightarrow & \color{red}{4} x& = & 29 \\\Leftrightarrow & x = \frac{29}{4} & & \\ & V = \left\{ \frac{29}{4} \right\} & \\\end{align}\)