Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-60} & = & \color{red}{220x} +66 \\\Leftrightarrow & 825x \color{red}{-60} \color{blue}{+60} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{+60} \\\Leftrightarrow & 825x-220x& = & 66+60 \\\Leftrightarrow & \color{red}{605} x& = & 126 \\\Leftrightarrow & x = \frac{126}{605} & & \\ & V = \left\{ \frac{126}{605} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -4x+\frac{4}{5} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -4x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{+12} & = & \color{red}{-20x} +4 \\\Leftrightarrow & 45x \color{red}{+12} \color{blue}{-12} \color{blue}{+20x} & = & \color{red}{-20x} +4 \color{blue}{+20x} \color{blue}{-12} \\\Leftrightarrow & 45x+20x& = & 4-12 \\\Leftrightarrow & \color{red}{65} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{65} & & \\ & V = \left\{ \frac{-8}{65} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{16}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-80} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 180x \color{red}{-80} \color{blue}{+80} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+80} \\\Leftrightarrow & 180x+75x& = & 18+80 \\\Leftrightarrow & \color{red}{255} x& = & 98 \\\Leftrightarrow & x = \frac{98}{255} & & \\ & V = \left\{ \frac{98}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -2x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-20x} +9 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{-24} \\\Leftrightarrow & 150x+20x& = & 9-24 \\\Leftrightarrow & \color{red}{170} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{170} & & \\\Leftrightarrow & x = \frac{-3}{34} & & \\ & V = \left\{ \frac{-3}{34} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & 63x+49x& = & 10-6 \\\Leftrightarrow & \color{red}{112} x& = & 4 \\\Leftrightarrow & x = \frac{4}{112} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{70x} +3 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -60x-70x& = & 3+12 \\\Leftrightarrow & \color{red}{-130} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-130} & & \\\Leftrightarrow & x = \frac{-3}{26} & & \\ & V = \left\{ \frac{-3}{26} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & -3x+\frac{7}{5} \\\Leftrightarrow & -18x+\frac{18}{11}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{-165x} +77 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{+165x} & = & \color{red}{-165x} +77 \color{blue}{+165x} \color{blue}{-90} \\\Leftrightarrow & -990x+165x& = & 77-90 \\\Leftrightarrow & \color{red}{-825} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-825} & & \\\Leftrightarrow & x = \frac{13}{825} & & \\ & V = \left\{ \frac{13}{825} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{+72} & = & \color{red}{-210x} +35 \\\Leftrightarrow & -480x \color{red}{+72} \color{blue}{-72} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-72} \\\Leftrightarrow & -480x+210x& = & 35-72 \\\Leftrightarrow & \color{red}{-270} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-270} & & \\\Leftrightarrow & x = \frac{37}{270} & & \\ & V = \left\{ \frac{37}{270} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{+105} & = & \color{red}{80x} +64 \\\Leftrightarrow & 1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-80x} & = & \color{red}{80x} +64 \color{blue}{-80x} \color{blue}{-105} \\\Leftrightarrow & 1400x-80x& = & 64-105 \\\Leftrightarrow & \color{red}{1320} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{1320} & & \\ & V = \left\{ \frac{-41}{1320} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & 360x+315x& = & 54+40 \\\Leftrightarrow & \color{red}{675} x& = & 94 \\\Leftrightarrow & x = \frac{94}{675} & & \\ & V = \left\{ \frac{94}{675} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{8}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-8} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{-8} \color{blue}{+8} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{+8} \\\Leftrightarrow & -132x+55x& = & 6+8 \\\Leftrightarrow & \color{red}{-77} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-77} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{4})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -14x+\frac{21}{4}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-56}{ \color{blue}{4} }x+ \frac{21}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -56x \color{red}{+21} & = & \color{red}{12x} +9 \\\Leftrightarrow & -56x \color{red}{+21} \color{blue}{-21} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{-21} \\\Leftrightarrow & -56x-12x& = & 9-21 \\\Leftrightarrow & \color{red}{-68} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-68} & & \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)