Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +56 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 56-150 \\\Leftrightarrow & \color{red}{-595} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-595} & & \\\Leftrightarrow & x = \frac{94}{595} & & \\ & V = \left\{ \frac{94}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{12})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{25}{12}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{+25} & = & \color{red}{108x} +40 \\\Leftrightarrow & -240x \color{red}{+25} \color{blue}{-25} \color{blue}{-108x} & = & \color{red}{108x} +40 \color{blue}{-108x} \color{blue}{-25} \\\Leftrightarrow & -240x-108x& = & 40-25 \\\Leftrightarrow & \color{red}{-348} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-348} & & \\\Leftrightarrow & x = \frac{-5}{116} & & \\ & V = \left\{ \frac{-5}{116} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{-60} & = & \color{red}{-45x} +5 \\\Leftrightarrow & -108x \color{red}{-60} \color{blue}{+60} \color{blue}{+45x} & = & \color{red}{-45x} +5 \color{blue}{+45x} \color{blue}{+60} \\\Leftrightarrow & -108x+45x& = & 5+60 \\\Leftrightarrow & \color{red}{-63} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-63} & & \\\Leftrightarrow & x = \frac{-65}{63} & & \\ & V = \left\{ \frac{-65}{63} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +3 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 3+24 \\\Leftrightarrow & \color{red}{70} x& = & 27 \\\Leftrightarrow & x = \frac{27}{70} & & \\ & V = \left\{ \frac{27}{70} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{4})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{25}{4}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{275}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+275} & = & \color{red}{-352x} +16 \\\Leftrightarrow & -660x \color{red}{+275} \color{blue}{-275} \color{blue}{+352x} & = & \color{red}{-352x} +16 \color{blue}{+352x} \color{blue}{-275} \\\Leftrightarrow & -660x+352x& = & 16-275 \\\Leftrightarrow & \color{red}{-308} x& = & -259 \\\Leftrightarrow & x = \frac{-259}{-308} & & \\\Leftrightarrow & x = \frac{37}{44} & & \\ & V = \left\{ \frac{37}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{11})& = & 8x+\frac{3}{8} \\\Leftrightarrow & -21x-\frac{28}{11}& = & 8x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{224}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-224} & = & \color{red}{704x} +33 \\\Leftrightarrow & -1848x \color{red}{-224} \color{blue}{+224} \color{blue}{-704x} & = & \color{red}{704x} +33 \color{blue}{-704x} \color{blue}{+224} \\\Leftrightarrow & -1848x-704x& = & 33+224 \\\Leftrightarrow & \color{red}{-2552} x& = & 257 \\\Leftrightarrow & x = \frac{257}{-2552} & & \\\Leftrightarrow & x = \frac{-257}{2552} & & \\ & V = \left\{ \frac{-257}{2552} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{15}{7}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+135} & = & \color{red}{126x} +70 \\\Leftrightarrow & 945x \color{red}{+135} \color{blue}{-135} \color{blue}{-126x} & = & \color{red}{126x} +70 \color{blue}{-126x} \color{blue}{-135} \\\Leftrightarrow & 945x-126x& = & 70-135 \\\Leftrightarrow & \color{red}{819} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{819} & & \\\Leftrightarrow & x = \frac{-5}{63} & & \\ & V = \left\{ \frac{-5}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{6}{5}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{-12} & = & \color{red}{-90x} +3 \\\Leftrightarrow & -40x \color{red}{-12} \color{blue}{+12} \color{blue}{+90x} & = & \color{red}{-90x} +3 \color{blue}{+90x} \color{blue}{+12} \\\Leftrightarrow & -40x+90x& = & 3+12 \\\Leftrightarrow & \color{red}{50} x& = & 15 \\\Leftrightarrow & x = \frac{15}{50} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+54} \\\Leftrightarrow & -270x+75x& = & 20+54 \\\Leftrightarrow & \color{red}{-195} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-195} & & \\\Leftrightarrow & x = \frac{-74}{195} & & \\ & V = \left\{ \frac{-74}{195} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 120x+25x& = & 6-24 \\\Leftrightarrow & \color{red}{145} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{145} & & \\ & V = \left\{ \frac{-18}{145} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{15}{7}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{-28x} +21 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{+28x} & = & \color{red}{-28x} +21 \color{blue}{+28x} \color{blue}{+30} \\\Leftrightarrow & 210x+28x& = & 21+30 \\\Leftrightarrow & \color{red}{238} x& = & 51 \\\Leftrightarrow & x = \frac{51}{238} & & \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{55} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)