Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{50x} +9 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{-18} \\\Leftrightarrow & 120x-50x& = & 9-18 \\\Leftrightarrow & \color{red}{70} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{70} & & \\ & V = \left\{ \frac{-9}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{231x} +28 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{+110} \\\Leftrightarrow & 770x-231x& = & 28+110 \\\Leftrightarrow & \color{red}{539} x& = & 138 \\\Leftrightarrow & x = \frac{138}{539} & & \\ & V = \left\{ \frac{138}{539} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{-567x} +56 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{-180} \\\Leftrightarrow & 1260x+567x& = & 56-180 \\\Leftrightarrow & \color{red}{1827} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{1827} & & \\ & V = \left\{ \frac{-124}{1827} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-108} & = & \color{red}{225x} +35 \\\Leftrightarrow & 810x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +35 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & 810x-225x& = & 35+108 \\\Leftrightarrow & \color{red}{585} x& = & 143 \\\Leftrightarrow & x = \frac{143}{585} & & \\\Leftrightarrow & x = \frac{11}{45} & & \\ & V = \left\{ \frac{11}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{5})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-9} & = & \color{red}{40x} +3 \\\Leftrightarrow & -75x \color{red}{-9} \color{blue}{+9} \color{blue}{-40x} & = & \color{red}{40x} +3 \color{blue}{-40x} \color{blue}{+9} \\\Leftrightarrow & -75x-40x& = & 3+9 \\\Leftrightarrow & \color{red}{-115} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-115} & & \\\Leftrightarrow & x = \frac{-12}{115} & & \\ & V = \left\{ \frac{-12}{115} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 18x-\frac{18}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1512}{ \color{blue}{84} }x- \frac{216}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1512x \color{red}{-216} & = & \color{red}{-588x} +49 \\\Leftrightarrow & 1512x \color{red}{-216} \color{blue}{+216} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{+216} \\\Leftrightarrow & 1512x+588x& = & 49+216 \\\Leftrightarrow & \color{red}{2100} x& = & 265 \\\Leftrightarrow & x = \frac{265}{2100} & & \\\Leftrightarrow & x = \frac{53}{420} & & \\ & V = \left\{ \frac{53}{420} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -25x-\frac{10}{3}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{-10} & = & \color{red}{-15x} +10 \\\Leftrightarrow & -75x \color{red}{-10} \color{blue}{+10} \color{blue}{+15x} & = & \color{red}{-15x} +10 \color{blue}{+15x} \color{blue}{+10} \\\Leftrightarrow & -75x+15x& = & 10+10 \\\Leftrightarrow & \color{red}{-60} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-60} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2016}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2016x \color{red}{+189} & = & \color{red}{-648x} +32 \\\Leftrightarrow & -2016x \color{red}{+189} \color{blue}{-189} \color{blue}{+648x} & = & \color{red}{-648x} +32 \color{blue}{+648x} \color{blue}{-189} \\\Leftrightarrow & -2016x+648x& = & 32-189 \\\Leftrightarrow & \color{red}{-1368} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-1368} & & \\\Leftrightarrow & x = \frac{157}{1368} & & \\ & V = \left\{ \frac{157}{1368} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{+72} & = & \color{red}{210x} +35 \\\Leftrightarrow & -480x \color{red}{+72} \color{blue}{-72} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{-72} \\\Leftrightarrow & -480x-210x& = & 35-72 \\\Leftrightarrow & \color{red}{-690} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-690} & & \\\Leftrightarrow & x = \frac{37}{690} & & \\ & V = \left\{ \frac{37}{690} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-10} & = & \color{red}{63x} +8 \\\Leftrightarrow & 140x \color{red}{-10} \color{blue}{+10} \color{blue}{-63x} & = & \color{red}{63x} +8 \color{blue}{-63x} \color{blue}{+10} \\\Leftrightarrow & 140x-63x& = & 8+10 \\\Leftrightarrow & \color{red}{77} x& = & 18 \\\Leftrightarrow & x = \frac{18}{77} & & \\ & V = \left\{ \frac{18}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+126} & = & \color{red}{539x} +88 \\\Leftrightarrow & -1386x \color{red}{+126} \color{blue}{-126} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-126} \\\Leftrightarrow & -1386x-539x& = & 88-126 \\\Leftrightarrow & \color{red}{-1925} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1925} & & \\\Leftrightarrow & x = \frac{38}{1925} & & \\ & V = \left\{ \frac{38}{1925} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{144}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-144} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -792x \color{red}{-144} \color{blue}{+144} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+144} \\\Leftrightarrow & -792x+297x& = & 44+144 \\\Leftrightarrow & \color{red}{-495} x& = & 188 \\\Leftrightarrow & x = \frac{188}{-495} & & \\\Leftrightarrow & x = \frac{-188}{495} & & \\ & V = \left\{ \frac{-188}{495} \right\} & \\\end{align}\)