Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-70x} +9 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & 60x+70x& = & 9-12 \\\Leftrightarrow & \color{red}{130} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{130} & & \\ & V = \left\{ \frac{-3}{130} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+4} & = & \color{red}{-45x} +30 \\\Leftrightarrow & -36x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +30 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & -36x+45x& = & 30-4 \\\Leftrightarrow & \color{red}{9} x& = & 26 \\\Leftrightarrow & x = \frac{26}{9} & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+66} & = & \color{red}{165x} +30 \\\Leftrightarrow & -440x \color{red}{+66} \color{blue}{-66} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{-66} \\\Leftrightarrow & -440x-165x& = & 30-66 \\\Leftrightarrow & \color{red}{-605} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-605} & & \\\Leftrightarrow & x = \frac{36}{605} & & \\ & V = \left\{ \frac{36}{605} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-132} & = & \color{red}{385x} +10 \\\Leftrightarrow & 330x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 330x-385x& = & 10+132 \\\Leftrightarrow & \color{red}{-55} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-55} & & \\\Leftrightarrow & x = \frac{-142}{55} & & \\ & V = \left\{ \frac{-142}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{18}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x+ \frac{144}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{+144} & = & \color{red}{280x} +63 \\\Leftrightarrow & -672x \color{red}{+144} \color{blue}{-144} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{-144} \\\Leftrightarrow & -672x-280x& = & 63-144 \\\Leftrightarrow & \color{red}{-952} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-952} & & \\\Leftrightarrow & x = \frac{81}{952} & & \\ & V = \left\{ \frac{81}{952} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 90x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{65} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{65} & & \\ & V = \left\{ \frac{-6}{65} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{70x} +21 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & 84x-70x& = & 21-12 \\\Leftrightarrow & \color{red}{14} x& = & 9 \\\Leftrightarrow & x = \frac{9}{14} & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 35x-\frac{21}{4}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{63}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-63} & = & \color{red}{36x} +40 \\\Leftrightarrow & 420x \color{red}{-63} \color{blue}{+63} \color{blue}{-36x} & = & \color{red}{36x} +40 \color{blue}{-36x} \color{blue}{+63} \\\Leftrightarrow & 420x-36x& = & 40+63 \\\Leftrightarrow & \color{red}{384} x& = & 103 \\\Leftrightarrow & x = \frac{103}{384} & & \\ & V = \left\{ \frac{103}{384} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1890x \color{red}{-270} & = & \color{red}{441x} +49 \\\Leftrightarrow & 1890x \color{red}{-270} \color{blue}{+270} \color{blue}{-441x} & = & \color{red}{441x} +49 \color{blue}{-441x} \color{blue}{+270} \\\Leftrightarrow & 1890x-441x& = & 49+270 \\\Leftrightarrow & \color{red}{1449} x& = & 319 \\\Leftrightarrow & x = \frac{319}{1449} & & \\ & V = \left\{ \frac{319}{1449} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -8x-\frac{4}{5}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-8} & = & \color{red}{-30x} +35 \\\Leftrightarrow & -80x \color{red}{-8} \color{blue}{+8} \color{blue}{+30x} & = & \color{red}{-30x} +35 \color{blue}{+30x} \color{blue}{+8} \\\Leftrightarrow & -80x+30x& = & 35+8 \\\Leftrightarrow & \color{red}{-50} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-50} & & \\\Leftrightarrow & x = \frac{-43}{50} & & \\ & V = \left\{ \frac{-43}{50} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{30}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+60} & = & \color{red}{154x} +99 \\\Leftrightarrow & 264x \color{red}{+60} \color{blue}{-60} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-60} \\\Leftrightarrow & 264x-154x& = & 99-60 \\\Leftrightarrow & \color{red}{110} x& = & 39 \\\Leftrightarrow & x = \frac{39}{110} & & \\ & V = \left\{ \frac{39}{110} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 8x+\frac{4}{9}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{576}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 576x \color{red}{+32} & = & \color{red}{-360x} +45 \\\Leftrightarrow & 576x \color{red}{+32} \color{blue}{-32} \color{blue}{+360x} & = & \color{red}{-360x} +45 \color{blue}{+360x} \color{blue}{-32} \\\Leftrightarrow & 576x+360x& = & 45-32 \\\Leftrightarrow & \color{red}{936} x& = & 13 \\\Leftrightarrow & x = \frac{13}{936} & & \\\Leftrightarrow & x = \frac{1}{72} & & \\ & V = \left\{ \frac{1}{72} \right\} & \\\end{align}\)