Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{196x} +12 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +12 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & -280x-196x& = & 12+105 \\\Leftrightarrow & \color{red}{-476} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-476} & & \\\Leftrightarrow & x = \frac{-117}{476} & & \\ & V = \left\{ \frac{-117}{476} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{3})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{16}{3}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-80} & = & \color{red}{-45x} +24 \\\Leftrightarrow & 120x \color{red}{-80} \color{blue}{+80} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{+80} \\\Leftrightarrow & 120x+45x& = & 24+80 \\\Leftrightarrow & \color{red}{165} x& = & 104 \\\Leftrightarrow & x = \frac{104}{165} & & \\ & V = \left\{ \frac{104}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{-8} & = & \color{red}{-21x} +4 \\\Leftrightarrow & -18x \color{red}{-8} \color{blue}{+8} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{+8} \\\Leftrightarrow & -18x+21x& = & 4+8 \\\Leftrightarrow & \color{red}{3} x& = & 12 \\\Leftrightarrow & x = \frac{12}{3} & & \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{12}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+48} & = & \color{red}{-196x} +21 \\\Leftrightarrow & 420x \color{red}{+48} \color{blue}{-48} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-48} \\\Leftrightarrow & 420x+196x& = & 21-48 \\\Leftrightarrow & \color{red}{616} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{616} & & \\ & V = \left\{ \frac{-27}{616} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{12})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{25}{12}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-25} & = & \color{red}{36x} +40 \\\Leftrightarrow & 120x \color{red}{-25} \color{blue}{+25} \color{blue}{-36x} & = & \color{red}{36x} +40 \color{blue}{-36x} \color{blue}{+25} \\\Leftrightarrow & 120x-36x& = & 40+25 \\\Leftrightarrow & \color{red}{84} x& = & 65 \\\Leftrightarrow & x = \frac{65}{84} & & \\ & V = \left\{ \frac{65}{84} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-56} & = & \color{red}{-105x} +6 \\\Leftrightarrow & 126x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & 126x+105x& = & 6+56 \\\Leftrightarrow & \color{red}{231} x& = & 62 \\\Leftrightarrow & x = \frac{62}{231} & & \\ & V = \left\{ \frac{62}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{200}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+200} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -840x \color{red}{+200} \color{blue}{-200} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-200} \\\Leftrightarrow & -840x+350x& = & 63-200 \\\Leftrightarrow & \color{red}{-490} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-490} & & \\\Leftrightarrow & x = \frac{137}{490} & & \\ & V = \left\{ \frac{137}{490} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{5})& = & -8x+\frac{3}{10} \\\Leftrightarrow & 35x+\frac{28}{5}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{56}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+56} & = & \color{red}{-80x} +3 \\\Leftrightarrow & 350x \color{red}{+56} \color{blue}{-56} \color{blue}{+80x} & = & \color{red}{-80x} +3 \color{blue}{+80x} \color{blue}{-56} \\\Leftrightarrow & 350x+80x& = & 3-56 \\\Leftrightarrow & \color{red}{430} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{430} & & \\ & V = \left\{ \frac{-53}{430} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+40} & = & \color{red}{42x} +9 \\\Leftrightarrow & -120x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & -120x-42x& = & 9-40 \\\Leftrightarrow & \color{red}{-162} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-162} & & \\\Leftrightarrow & x = \frac{31}{162} & & \\ & V = \left\{ \frac{31}{162} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -4x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+18} & = & \color{red}{-132x} +22 \\\Leftrightarrow & -495x \color{red}{+18} \color{blue}{-18} \color{blue}{+132x} & = & \color{red}{-132x} +22 \color{blue}{+132x} \color{blue}{-18} \\\Leftrightarrow & -495x+132x& = & 22-18 \\\Leftrightarrow & \color{red}{-363} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-363} & & \\\Leftrightarrow & x = \frac{-4}{363} & & \\ & V = \left\{ \frac{-4}{363} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-72} & = & \color{red}{693x} +110 \\\Leftrightarrow & -594x \color{red}{-72} \color{blue}{+72} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+72} \\\Leftrightarrow & -594x-693x& = & 110+72 \\\Leftrightarrow & \color{red}{-1287} x& = & 182 \\\Leftrightarrow & x = \frac{182}{-1287} & & \\\Leftrightarrow & x = \frac{-14}{99} & & \\ & V = \left\{ \frac{-14}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{+42} & = & \color{red}{-45x} +20 \\\Leftrightarrow & 210x \color{red}{+42} \color{blue}{-42} \color{blue}{+45x} & = & \color{red}{-45x} +20 \color{blue}{+45x} \color{blue}{-42} \\\Leftrightarrow & 210x+45x& = & 20-42 \\\Leftrightarrow & \color{red}{255} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{255} & & \\ & V = \left\{ \frac{-22}{255} \right\} & \\\end{align}\)