Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{35x} +10 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -63x-35x& = & 10+6 \\\Leftrightarrow & \color{red}{-98} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-98} & & \\\Leftrightarrow & x = \frac{-8}{49} & & \\ & V = \left\{ \frac{-8}{49} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & -3x+\frac{7}{5} \\\Leftrightarrow & 20x-\frac{8}{9}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-40} & = & \color{red}{-135x} +63 \\\Leftrightarrow & 900x \color{red}{-40} \color{blue}{+40} \color{blue}{+135x} & = & \color{red}{-135x} +63 \color{blue}{+135x} \color{blue}{+40} \\\Leftrightarrow & 900x+135x& = & 63+40 \\\Leftrightarrow & \color{red}{1035} x& = & 103 \\\Leftrightarrow & x = \frac{103}{1035} & & \\ & V = \left\{ \frac{103}{1035} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{7})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+128} & = & \color{red}{-392x} +35 \\\Leftrightarrow & -1120x \color{red}{+128} \color{blue}{-128} \color{blue}{+392x} & = & \color{red}{-392x} +35 \color{blue}{+392x} \color{blue}{-128} \\\Leftrightarrow & -1120x+392x& = & 35-128 \\\Leftrightarrow & \color{red}{-728} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-728} & & \\\Leftrightarrow & x = \frac{93}{728} & & \\ & V = \left\{ \frac{93}{728} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{+154} & = & \color{red}{-165x} +50 \\\Leftrightarrow & 770x \color{red}{+154} \color{blue}{-154} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{-154} \\\Leftrightarrow & 770x+165x& = & 50-154 \\\Leftrightarrow & \color{red}{935} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{935} & & \\ & V = \left\{ \frac{-104}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{7})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{12}{7}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+36} & = & \color{red}{168x} +14 \\\Leftrightarrow & 189x \color{red}{+36} \color{blue}{-36} \color{blue}{-168x} & = & \color{red}{168x} +14 \color{blue}{-168x} \color{blue}{-36} \\\Leftrightarrow & 189x-168x& = & 14-36 \\\Leftrightarrow & \color{red}{21} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+108} & = & \color{red}{225x} +20 \\\Leftrightarrow & 540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & 540x-225x& = & 20-108 \\\Leftrightarrow & \color{red}{315} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{315} & & \\ & V = \left\{ \frac{-88}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -18x-\frac{18}{5}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1080}{ \color{blue}{60} }x- \frac{216}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1080x \color{red}{-216} & = & \color{red}{420x} +35 \\\Leftrightarrow & -1080x \color{red}{-216} \color{blue}{+216} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{+216} \\\Leftrightarrow & -1080x-420x& = & 35+216 \\\Leftrightarrow & \color{red}{-1500} x& = & 251 \\\Leftrightarrow & x = \frac{251}{-1500} & & \\\Leftrightarrow & x = \frac{-251}{1500} & & \\ & V = \left\{ \frac{-251}{1500} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{3})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{8}{3}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{165x} +15 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{+88} \\\Leftrightarrow & 396x-165x& = & 15+88 \\\Leftrightarrow & \color{red}{231} x& = & 103 \\\Leftrightarrow & x = \frac{103}{231} & & \\ & V = \left\{ \frac{103}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & 504x+315x& = & 18-56 \\\Leftrightarrow & \color{red}{819} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{819} & & \\ & V = \left\{ \frac{-38}{819} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{12})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{25}{12}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+25} & = & \color{red}{-36x} +54 \\\Leftrightarrow & 300x \color{red}{+25} \color{blue}{-25} \color{blue}{+36x} & = & \color{red}{-36x} +54 \color{blue}{+36x} \color{blue}{-25} \\\Leftrightarrow & 300x+36x& = & 54-25 \\\Leftrightarrow & \color{red}{336} x& = & 29 \\\Leftrightarrow & x = \frac{29}{336} & & \\ & V = \left\{ \frac{29}{336} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{-50x} +3 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 240x+50x& = & 3+24 \\\Leftrightarrow & \color{red}{290} x& = & 27 \\\Leftrightarrow & x = \frac{27}{290} & & \\ & V = \left\{ \frac{27}{290} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & -2x+\frac{5}{3} \\\Leftrightarrow & 9x+\frac{9}{10}& = & -2x+\frac{5}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{-60}{ \color{blue}{30} }x+ \frac{50}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{+27} & = & \color{red}{-60x} +50 \\\Leftrightarrow & 270x \color{red}{+27} \color{blue}{-27} \color{blue}{+60x} & = & \color{red}{-60x} +50 \color{blue}{+60x} \color{blue}{-27} \\\Leftrightarrow & 270x+60x& = & 50-27 \\\Leftrightarrow & \color{red}{330} x& = & 23 \\\Leftrightarrow & x = \frac{23}{330} & & \\ & V = \left\{ \frac{23}{330} \right\} & \\\end{align}\)