Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{8}{9}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{45x} +30 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +30 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 36x-45x& = & 30-8 \\\Leftrightarrow & \color{red}{-9} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-9} & & \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+12} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -56x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & -56x+70x& = & 35-12 \\\Leftrightarrow & \color{red}{14} x& = & 23 \\\Leftrightarrow & x = \frac{23}{14} & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -16x-\frac{16}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-80} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -880x \color{red}{-80} \color{blue}{+80} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+80} \\\Leftrightarrow & -880x+385x& = & 22+80 \\\Leftrightarrow & \color{red}{-495} x& = & 102 \\\Leftrightarrow & x = \frac{102}{-495} & & \\\Leftrightarrow & x = \frac{-34}{165} & & \\ & V = \left\{ \frac{-34}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-60} & = & \color{red}{63x} +4 \\\Leftrightarrow & 72x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & 72x-63x& = & 4+60 \\\Leftrightarrow & \color{red}{9} x& = & 64 \\\Leftrightarrow & x = \frac{64}{9} & & \\ & V = \left\{ \frac{64}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & -8x+\frac{7}{4} \\\Leftrightarrow & -21x-\frac{14}{9}& = & -8x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-756}{ \color{blue}{36} }x- \frac{56}{ \color{blue}{36} })& = & (\frac{-288}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -756x \color{red}{-56} & = & \color{red}{-288x} +63 \\\Leftrightarrow & -756x \color{red}{-56} \color{blue}{+56} \color{blue}{+288x} & = & \color{red}{-288x} +63 \color{blue}{+288x} \color{blue}{+56} \\\Leftrightarrow & -756x+288x& = & 63+56 \\\Leftrightarrow & \color{red}{-468} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-468} & & \\\Leftrightarrow & x = \frac{-119}{468} & & \\ & V = \left\{ \frac{-119}{468} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{7})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{8}{7}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{72}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-72} & = & \color{red}{-567x} +14 \\\Leftrightarrow & 504x \color{red}{-72} \color{blue}{+72} \color{blue}{+567x} & = & \color{red}{-567x} +14 \color{blue}{+567x} \color{blue}{+72} \\\Leftrightarrow & 504x+567x& = & 14+72 \\\Leftrightarrow & \color{red}{1071} x& = & 86 \\\Leftrightarrow & x = \frac{86}{1071} & & \\ & V = \left\{ \frac{86}{1071} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{9})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{10}{9}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-70} & = & \color{red}{-441x} +90 \\\Leftrightarrow & 1260x \color{red}{-70} \color{blue}{+70} \color{blue}{+441x} & = & \color{red}{-441x} +90 \color{blue}{+441x} \color{blue}{+70} \\\Leftrightarrow & 1260x+441x& = & 90+70 \\\Leftrightarrow & \color{red}{1701} x& = & 160 \\\Leftrightarrow & x = \frac{160}{1701} & & \\ & V = \left\{ \frac{160}{1701} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{9})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 21x-\frac{35}{9}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{378}{ \color{blue}{18} }x- \frac{70}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 378x \color{red}{-70} & = & \color{red}{36x} +63 \\\Leftrightarrow & 378x \color{red}{-70} \color{blue}{+70} \color{blue}{-36x} & = & \color{red}{36x} +63 \color{blue}{-36x} \color{blue}{+70} \\\Leftrightarrow & 378x-36x& = & 63+70 \\\Leftrightarrow & \color{red}{342} x& = & 133 \\\Leftrightarrow & x = \frac{133}{342} & & \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 540x+225x& = & 50+108 \\\Leftrightarrow & \color{red}{765} x& = & 158 \\\Leftrightarrow & x = \frac{158}{765} & & \\ & V = \left\{ \frac{158}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{9})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{8}{9}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+40} & = & \color{red}{-225x} +72 \\\Leftrightarrow & 540x \color{red}{+40} \color{blue}{-40} \color{blue}{+225x} & = & \color{red}{-225x} +72 \color{blue}{+225x} \color{blue}{-40} \\\Leftrightarrow & 540x+225x& = & 72-40 \\\Leftrightarrow & \color{red}{765} x& = & 32 \\\Leftrightarrow & x = \frac{32}{765} & & \\ & V = \left\{ \frac{32}{765} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{270x} +27 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{-100} \\\Leftrightarrow & 240x-270x& = & 27-100 \\\Leftrightarrow & \color{red}{-30} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-30} & & \\\Leftrightarrow & x = \frac{73}{30} & & \\ & V = \left\{ \frac{73}{30} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & -4x+\frac{2}{5} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-50} & = & \color{red}{-140x} +14 \\\Leftrightarrow & -525x \color{red}{-50} \color{blue}{+50} \color{blue}{+140x} & = & \color{red}{-140x} +14 \color{blue}{+140x} \color{blue}{+50} \\\Leftrightarrow & -525x+140x& = & 14+50 \\\Leftrightarrow & \color{red}{-385} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-385} & & \\\Leftrightarrow & x = \frac{-64}{385} & & \\ & V = \left\{ \frac{-64}{385} \right\} & \\\end{align}\)