# Vgln. eerste graad (reeks 5)

#### Alles samen. Gebruik stappenplan en ZRM!

1. $$3(-x-\frac{4}{15})=-2x+\frac{3}{14}$$
2. $$-6(-4x+\frac{4}{11})=x+\frac{4}{3}$$
3. $$2(-4x-\frac{4}{15})=9x+\frac{4}{13}$$
4. $$-5(2x-\frac{2}{5})=x+\frac{5}{12}$$
5. $$-5(2x+\frac{4}{3})=7x+\frac{10}{3}$$
6. $$2(x+\frac{2}{3})=3x+\frac{2}{3}$$
7. $$4(3x-\frac{3}{2})=x+\frac{6}{5}$$
8. $$-3(-x+\frac{3}{10})=5x+\frac{6}{11}$$
9. $$-5(-4x-\frac{2}{9})=x+\frac{3}{13}$$
10. $$7(-3x-\frac{2}{7})=-4x+\frac{2}{13}$$
11. $$-5(-4x+\frac{5}{6})=3x+\frac{2}{9}$$
12. $$-7(2x-\frac{5}{4})=-9x+\frac{8}{9}$$

#### Alles samen. Gebruik stappenplan en ZRM!

##### Verbetersleutel

1. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-x-\frac{4}{15})& = & -2x+\frac{3}{14} \\\Leftrightarrow & -3x-\frac{4}{5}& = & -2x+\frac{3}{14} \\ & & & \text{kgv van noemers 5 en 14 is 70} \\\Leftrightarrow & \color{blue}{70} .(-3x-\frac{4}{5})& = & (-2x+\frac{3}{14}). \color{blue}{70} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{-140x} +15 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+56} \\\Leftrightarrow & -210x+140x& = & 15+56 \\\Leftrightarrow & \color{red}{-70} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-70} & & \\\Leftrightarrow & x = \frac{-71}{70} & & \\ & V = \left\{ \frac{-71}{70} \right\} & \\\end{align}
2. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & x+\frac{4}{3} \\\Leftrightarrow & 24x-\frac{24}{11}& = & x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(24x-\frac{24}{11})& = & (x+\frac{4}{3}). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{33x} +44 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-33x} & = & \color{red}{33x} +44 \color{blue}{-33x} \color{blue}{+72} \\\Leftrightarrow & 792x-33x& = & 44+72 \\\Leftrightarrow & \color{red}{759} x& = & 116 \\\Leftrightarrow & x = \frac{116}{759} & & \\ & V = \left\{ \frac{116}{759} \right\} & \\\end{align}
3. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{15})& = & 9x+\frac{4}{13} \\\Leftrightarrow & -8x-\frac{8}{15}& = & 9x+\frac{4}{13} \\ & & & \text{kgv van noemers 15 en 13 is 195} \\\Leftrightarrow & \color{blue}{195} .(-8x-\frac{8}{15})& = & (9x+\frac{4}{13}). \color{blue}{195} \\\Leftrightarrow & -1560x \color{red}{-104} & = & \color{red}{1755x} +60 \\\Leftrightarrow & -1560x \color{red}{-104} \color{blue}{+104} \color{blue}{-1755x} & = & \color{red}{1755x} +60 \color{blue}{-1755x} \color{blue}{+104} \\\Leftrightarrow & -1560x-1755x& = & 60+104 \\\Leftrightarrow & \color{red}{-3315} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-3315} & & \\\Leftrightarrow & x = \frac{-164}{3315} & & \\ & V = \left\{ \frac{-164}{3315} \right\} & \\\end{align}
4. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{5})& = & x+\frac{5}{12} \\\Leftrightarrow & -10x+2& = & x+\frac{5}{12} \\ & & & \text{kgv van noemers 1 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(-10x+2)& = & (x+\frac{5}{12}). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{12x} +5 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-12x} & = & \color{red}{12x} +5 \color{blue}{-12x} \color{blue}{-24} \\\Leftrightarrow & -120x-12x& = & 5-24 \\\Leftrightarrow & \color{red}{-132} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-132} & & \\\Leftrightarrow & x = \frac{19}{132} & & \\ & V = \left\{ \frac{19}{132} \right\} & \\\end{align}
5. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(-10x-\frac{20}{3})& = & (7x+\frac{10}{3}). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-20} & = & \color{red}{21x} +10 \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & -30x-21x& = & 10+20 \\\Leftrightarrow & \color{red}{-51} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-51} & & \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}
6. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 2x+\frac{4}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(2x+\frac{4}{3})& = & (3x+\frac{2}{3}). \color{blue}{3} \\\Leftrightarrow & 6x \color{red}{+4} & = & \color{red}{9x} +2 \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-4} \\\Leftrightarrow & 6x-9x& = & 2-4 \\\Leftrightarrow & \color{red}{-3} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-3} & & \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}
7. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{2})& = & x+\frac{6}{5} \\\Leftrightarrow & 12x-6& = & x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(12x-6)& = & (x+\frac{6}{5}). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-30} & = & \color{red}{5x} +6 \\\Leftrightarrow & 60x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = & \color{red}{5x} +6 \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 60x-5x& = & 6+30 \\\Leftrightarrow & \color{red}{55} x& = & 36 \\\Leftrightarrow & x = \frac{36}{55} & & \\ & V = \left\{ \frac{36}{55} \right\} & \\\end{align}
8. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-x+\frac{3}{10})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 3x-\frac{9}{10}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(3x-\frac{9}{10})& = & (5x+\frac{6}{11}). \color{blue}{110} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{550x} +60 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +60 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & 330x-550x& = & 60+99 \\\Leftrightarrow & \color{red}{-220} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-220} & & \\\Leftrightarrow & x = \frac{-159}{220} & & \\ & V = \left\{ \frac{-159}{220} \right\} & \\\end{align}
9. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{9})& = & x+\frac{3}{13} \\\Leftrightarrow & 20x+\frac{10}{9}& = & x+\frac{3}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(20x+\frac{10}{9})& = & (x+\frac{3}{13}). \color{blue}{117} \\\Leftrightarrow & 2340x \color{red}{+130} & = & \color{red}{117x} +27 \\\Leftrightarrow & 2340x \color{red}{+130} \color{blue}{-130} \color{blue}{-117x} & = & \color{red}{117x} +27 \color{blue}{-117x} \color{blue}{-130} \\\Leftrightarrow & 2340x-117x& = & 27-130 \\\Leftrightarrow & \color{red}{2223} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{2223} & & \\ & V = \left\{ \frac{-103}{2223} \right\} & \\\end{align}
10. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{7})& = & -4x+\frac{2}{13} \\\Leftrightarrow & -21x-2& = & -4x+\frac{2}{13} \\ & & & \text{kgv van noemers 1 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(-21x-2)& = & (-4x+\frac{2}{13}). \color{blue}{13} \\\Leftrightarrow & -273x \color{red}{-26} & = & \color{red}{-52x} +2 \\\Leftrightarrow & -273x \color{red}{-26} \color{blue}{+26} \color{blue}{+52x} & = & \color{red}{-52x} +2 \color{blue}{+52x} \color{blue}{+26} \\\Leftrightarrow & -273x+52x& = & 2+26 \\\Leftrightarrow & \color{red}{-221} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-221} & & \\\Leftrightarrow & x = \frac{-28}{221} & & \\ & V = \left\{ \frac{-28}{221} \right\} & \\\end{align}
11. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{6})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(20x-\frac{25}{6})& = & (3x+\frac{2}{9}). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-75} & = & \color{red}{54x} +4 \\\Leftrightarrow & 360x \color{red}{-75} \color{blue}{+75} \color{blue}{-54x} & = & \color{red}{54x} +4 \color{blue}{-54x} \color{blue}{+75} \\\Leftrightarrow & 360x-54x& = & 4+75 \\\Leftrightarrow & \color{red}{306} x& = & 79 \\\Leftrightarrow & x = \frac{79}{306} & & \\ & V = \left\{ \frac{79}{306} \right\} & \\\end{align}
12. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{4})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -14x+\frac{35}{4}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(-14x+\frac{35}{4})& = & (-9x+\frac{8}{9}). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+315} & = & \color{red}{-324x} +32 \\\Leftrightarrow & -504x \color{red}{+315} \color{blue}{-315} \color{blue}{+324x} & = & \color{red}{-324x} +32 \color{blue}{+324x} \color{blue}{-315} \\\Leftrightarrow & -504x+324x& = & 32-315 \\\Leftrightarrow & \color{red}{-180} x& = & -283 \\\Leftrightarrow & x = \frac{-283}{-180} & & \\\Leftrightarrow & x = \frac{283}{180} & & \\ & V = \left\{ \frac{283}{180} \right\} & \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2023-06-07 16:46:48