Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{9}{11} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-132} & = & \color{red}{-385x} +45 \\\Leftrightarrow & -880x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +45 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -880x+385x& = & 45+132 \\\Leftrightarrow & \color{red}{-495} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-495} & & \\\Leftrightarrow & x = \frac{-59}{165} & & \\ & V = \left\{ \frac{-59}{165} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{8}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+40} & = & \color{red}{-75x} +18 \\\Leftrightarrow & -180x \color{red}{+40} \color{blue}{-40} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{-40} \\\Leftrightarrow & -180x+75x& = & 18-40 \\\Leftrightarrow & \color{red}{-105} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-105} & & \\\Leftrightarrow & x = \frac{22}{105} & & \\ & V = \left\{ \frac{22}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 14x+\frac{28}{9}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{+196} & = & \color{red}{-189x} +54 \\\Leftrightarrow & 882x \color{red}{+196} \color{blue}{-196} \color{blue}{+189x} & = & \color{red}{-189x} +54 \color{blue}{+189x} \color{blue}{-196} \\\Leftrightarrow & 882x+189x& = & 54-196 \\\Leftrightarrow & \color{red}{1071} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{1071} & & \\ & V = \left\{ \frac{-142}{1071} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{+270} & = & \color{red}{693x} +44 \\\Leftrightarrow & 1782x \color{red}{+270} \color{blue}{-270} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-270} \\\Leftrightarrow & 1782x-693x& = & 44-270 \\\Leftrightarrow & \color{red}{1089} x& = & -226 \\\Leftrightarrow & x = \frac{-226}{1089} & & \\ & V = \left\{ \frac{-226}{1089} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{385x} +40 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -1650x-385x& = & 40+132 \\\Leftrightarrow & \color{red}{-2035} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-2035} & & \\\Leftrightarrow & x = \frac{-172}{2035} & & \\ & V = \left\{ \frac{-172}{2035} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-396}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -396x \color{red}{+24} & = & \color{red}{220x} +33 \\\Leftrightarrow & -396x \color{red}{+24} \color{blue}{-24} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{-24} \\\Leftrightarrow & -396x-220x& = & 33-24 \\\Leftrightarrow & \color{red}{-616} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-616} & & \\\Leftrightarrow & x = \frac{-9}{616} & & \\ & V = \left\{ \frac{-9}{616} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{10}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-10} & = & \color{red}{-21x} +4 \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & 30x+21x& = & 4+10 \\\Leftrightarrow & \color{red}{51} x& = & 14 \\\Leftrightarrow & x = \frac{14}{51} & & \\ & V = \left\{ \frac{14}{51} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -18x+\frac{18}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-540}{ \color{blue}{30} }x+ \frac{108}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-108} \\\Leftrightarrow & -540x+150x& = & 25-108 \\\Leftrightarrow & \color{red}{-390} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-390} & & \\\Leftrightarrow & x = \frac{83}{390} & & \\ & V = \left\{ \frac{83}{390} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{20}{3}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+80} & = & \color{red}{-84x} +9 \\\Leftrightarrow & 180x \color{red}{+80} \color{blue}{-80} \color{blue}{+84x} & = & \color{red}{-84x} +9 \color{blue}{+84x} \color{blue}{-80} \\\Leftrightarrow & 180x+84x& = & 9-80 \\\Leftrightarrow & \color{red}{264} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{264} & & \\ & V = \left\{ \frac{-71}{264} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -25x-\frac{15}{2}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{-105} & = & \color{red}{126x} +8 \\\Leftrightarrow & -350x \color{red}{-105} \color{blue}{+105} \color{blue}{-126x} & = & \color{red}{126x} +8 \color{blue}{-126x} \color{blue}{+105} \\\Leftrightarrow & -350x-126x& = & 8+105 \\\Leftrightarrow & \color{red}{-476} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-476} & & \\\Leftrightarrow & x = \frac{-113}{476} & & \\ & V = \left\{ \frac{-113}{476} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & -8x+\frac{3}{5} \\\Leftrightarrow & -15x-\frac{9}{5}& = & -8x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-9} & = & \color{red}{-40x} +3 \\\Leftrightarrow & -75x \color{red}{-9} \color{blue}{+9} \color{blue}{+40x} & = & \color{red}{-40x} +3 \color{blue}{+40x} \color{blue}{+9} \\\Leftrightarrow & -75x+40x& = & 3+9 \\\Leftrightarrow & \color{red}{-35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-35} & & \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1344}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1344x \color{red}{-240} & = & \color{red}{-280x} +21 \\\Leftrightarrow & 1344x \color{red}{-240} \color{blue}{+240} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{+240} \\\Leftrightarrow & 1344x+280x& = & 21+240 \\\Leftrightarrow & \color{red}{1624} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1624} & & \\\Leftrightarrow & x = \frac{9}{56} & & \\ & V = \left\{ \frac{9}{56} \right\} & \\\end{align}\)