# Vgln. eerste graad (reeks 5)

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

1. $$-6(-5x-\frac{4}{7})=29x+\frac{5}{7}$$
2. $$-6(-3x-\frac{5}{2})=7x+\frac{2}{15}$$
3. $$-2(4x-\frac{5}{13})=x+\frac{3}{8}$$
4. $$-4(4x+\frac{4}{5})=-9x+\frac{3}{5}$$
5. $$7(2x-\frac{4}{15})=-9x+\frac{5}{8}$$
6. $$3(3x+\frac{2}{15})=10x+\frac{9}{10}$$
7. $$5(-2x-\frac{4}{7})=-3x+\frac{5}{8}$$
8. $$5(-2x-\frac{4}{7})=3x+\frac{4}{5}$$
9. $$-7(-4x-\frac{4}{9})=-9x+\frac{10}{11}$$
10. $$6(2x-\frac{2}{7})=7x+\frac{6}{7}$$
11. $$7(3x+\frac{4}{15})=4x+\frac{10}{9}$$
12. $$3(-5x+\frac{5}{16})=-7x+\frac{6}{11}$$

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

##### Verbetersleutel

1. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{7})& = & 29x+\frac{5}{7} \\\Leftrightarrow & 30x+\frac{24}{7}& = & 29x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(30x+\frac{24}{7})& = & (29x+\frac{5}{7}). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{+24} & = & \color{red}{203x} +5 \\\Leftrightarrow & 210x \color{red}{+24} \color{blue}{-24} \color{blue}{-203x} & = & \color{red}{203x} +5 \color{blue}{-203x} \color{blue}{-24} \\\Leftrightarrow & 210x-203x& = & 5-24 \\\Leftrightarrow & \color{red}{7} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{7} & & \\\end{align}
2. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{2})& = & 7x+\frac{2}{15} \\\Leftrightarrow & 18x+15& = & 7x+\frac{2}{15} \\ & & & \text{kgv van noemers 1 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(18x+15)& = & (7x+\frac{2}{15}). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+225} & = & \color{red}{105x} +2 \\\Leftrightarrow & 270x \color{red}{+225} \color{blue}{-225} \color{blue}{-105x} & = & \color{red}{105x} +2 \color{blue}{-105x} \color{blue}{-225} \\\Leftrightarrow & 270x-105x& = & 2-225 \\\Leftrightarrow & \color{red}{165} x& = & -223 \\\Leftrightarrow & x = \frac{-223}{165} & & \\\end{align}
3. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{13})& = & x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{10}{13}& = & x+\frac{3}{8} \\ & & & \text{kgv van noemers 13 en 8 is 104} \\\Leftrightarrow & \color{blue}{104} .(-8x+\frac{10}{13})& = & (x+\frac{3}{8}). \color{blue}{104} \\\Leftrightarrow & -832x \color{red}{+80} & = & \color{red}{104x} +39 \\\Leftrightarrow & -832x \color{red}{+80} \color{blue}{-80} \color{blue}{-104x} & = & \color{red}{104x} +39 \color{blue}{-104x} \color{blue}{-80} \\\Leftrightarrow & -832x-104x& = & 39-80 \\\Leftrightarrow & \color{red}{-936} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-936} & & \\\Leftrightarrow & x = \frac{41}{936} & & \\\end{align}
4. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{5})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -16x-\frac{16}{5}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(-16x-\frac{16}{5})& = & (-9x+\frac{3}{5}). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{-45x} +3 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{+45x} & = & \color{red}{-45x} +3 \color{blue}{+45x} \color{blue}{+16} \\\Leftrightarrow & -80x+45x& = & 3+16 \\\Leftrightarrow & \color{red}{-35} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-35} & & \\\Leftrightarrow & x = \frac{-19}{35} & & \\\end{align}
5. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{15})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 14x-\frac{28}{15}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 15 en 8 is 120} \\\Leftrightarrow & \color{blue}{120} .(14x-\frac{28}{15})& = & (-9x+\frac{5}{8}). \color{blue}{120} \\\Leftrightarrow & 1680x \color{red}{-224} & = & \color{red}{-1080x} +75 \\\Leftrightarrow & 1680x \color{red}{-224} \color{blue}{+224} \color{blue}{+1080x} & = & \color{red}{-1080x} +75 \color{blue}{+1080x} \color{blue}{+224} \\\Leftrightarrow & 1680x+1080x& = & 75+224 \\\Leftrightarrow & \color{red}{2760} x& = & 299 \\\Leftrightarrow & x = \frac{299}{2760} & & \\\Leftrightarrow & x = \frac{13}{120} & & \\\end{align}
6. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{15})& = & 10x+\frac{9}{10} \\\Leftrightarrow & 9x+\frac{2}{5}& = & 10x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(9x+\frac{2}{5})& = & (10x+\frac{9}{10}). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+4} & = & \color{red}{100x} +9 \\\Leftrightarrow & 90x \color{red}{+4} \color{blue}{-4} \color{blue}{-100x} & = & \color{red}{100x} +9 \color{blue}{-100x} \color{blue}{-4} \\\Leftrightarrow & 90x-100x& = & 9-4 \\\Leftrightarrow & \color{red}{-10} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-10} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\\end{align}
7. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & -3x+\frac{5}{8} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -3x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(-10x-\frac{20}{7})& = & (-3x+\frac{5}{8}). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{-160} & = & \color{red}{-168x} +35 \\\Leftrightarrow & -560x \color{red}{-160} \color{blue}{+160} \color{blue}{+168x} & = & \color{red}{-168x} +35 \color{blue}{+168x} \color{blue}{+160} \\\Leftrightarrow & -560x+168x& = & 35+160 \\\Leftrightarrow & \color{red}{-392} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-392} & & \\\Leftrightarrow & x = \frac{-195}{392} & & \\\end{align}
8. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(-10x-\frac{20}{7})& = & (3x+\frac{4}{5}). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-100} & = & \color{red}{105x} +28 \\\Leftrightarrow & -350x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & -350x-105x& = & 28+100 \\\Leftrightarrow & \color{red}{-455} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-455} & & \\\Leftrightarrow & x = \frac{-128}{455} & & \\\end{align}
9. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{9})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(28x+\frac{28}{9})& = & (-9x+\frac{10}{11}). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{+308} & = & \color{red}{-891x} +90 \\\Leftrightarrow & 2772x \color{red}{+308} \color{blue}{-308} \color{blue}{+891x} & = & \color{red}{-891x} +90 \color{blue}{+891x} \color{blue}{-308} \\\Leftrightarrow & 2772x+891x& = & 90-308 \\\Leftrightarrow & \color{red}{3663} x& = & -218 \\\Leftrightarrow & x = \frac{-218}{3663} & & \\\end{align}
10. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(12x-\frac{12}{7})& = & (7x+\frac{6}{7}). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{49x} +6 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+12} \\\Leftrightarrow & 84x-49x& = & 6+12 \\\Leftrightarrow & \color{red}{35} x& = & 18 \\\Leftrightarrow & x = \frac{18}{35} & & \\\end{align}
11. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{15})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 21x+\frac{28}{15}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 15 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(21x+\frac{28}{15})& = & (4x+\frac{10}{9}). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+84} & = & \color{red}{180x} +50 \\\Leftrightarrow & 945x \color{red}{+84} \color{blue}{-84} \color{blue}{-180x} & = & \color{red}{180x} +50 \color{blue}{-180x} \color{blue}{-84} \\\Leftrightarrow & 945x-180x& = & 50-84 \\\Leftrightarrow & \color{red}{765} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{765} & & \\\Leftrightarrow & x = \frac{-2}{45} & & \\\end{align}
12. \text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{16})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{15}{16}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 16 en 11 is 176} \\\Leftrightarrow & \color{blue}{176} .(-15x+\frac{15}{16})& = & (-7x+\frac{6}{11}). \color{blue}{176} \\\Leftrightarrow & -2640x \color{red}{+165} & = & \color{red}{-1232x} +96 \\\Leftrightarrow & -2640x \color{red}{+165} \color{blue}{-165} \color{blue}{+1232x} & = & \color{red}{-1232x} +96 \color{blue}{+1232x} \color{blue}{-165} \\\Leftrightarrow & -2640x+1232x& = & 96-165 \\\Leftrightarrow & \color{red}{-1408} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-1408} & & \\\Leftrightarrow & x = \frac{69}{1408} & & \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2022-05-24 04:01:14