Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{5})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{14}{5}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-42} & = & \color{red}{-60x} +10 \\\Leftrightarrow & 525x \color{red}{-42} \color{blue}{+42} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{+42} \\\Leftrightarrow & 525x+60x& = & 10+42 \\\Leftrightarrow & \color{red}{585} x& = & 52 \\\Leftrightarrow & x = \frac{52}{585} & & \\\Leftrightarrow & x = \frac{4}{45} & & \\ & V = \left\{ \frac{4}{45} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -30x+\frac{12}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-420}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -420x \color{red}{+24} & = & \color{red}{-98x} +49 \\\Leftrightarrow & -420x \color{red}{+24} \color{blue}{-24} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{-24} \\\Leftrightarrow & -420x+98x& = & 49-24 \\\Leftrightarrow & \color{red}{-322} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-322} & & \\\Leftrightarrow & x = \frac{-25}{322} & & \\ & V = \left\{ \frac{-25}{322} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{2})& = & 2x+\frac{4}{9} \\\Leftrightarrow & 35x-\frac{21}{2}& = & 2x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{630}{ \color{blue}{18} }x- \frac{189}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 630x \color{red}{-189} & = & \color{red}{36x} +8 \\\Leftrightarrow & 630x \color{red}{-189} \color{blue}{+189} \color{blue}{-36x} & = & \color{red}{36x} +8 \color{blue}{-36x} \color{blue}{+189} \\\Leftrightarrow & 630x-36x& = & 8+189 \\\Leftrightarrow & \color{red}{594} x& = & 197 \\\Leftrightarrow & x = \frac{197}{594} & & \\ & V = \left\{ \frac{197}{594} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & -8x+\frac{7}{9} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-42} & = & \color{red}{-72x} +7 \\\Leftrightarrow & 189x \color{red}{-42} \color{blue}{+42} \color{blue}{+72x} & = & \color{red}{-72x} +7 \color{blue}{+72x} \color{blue}{+42} \\\Leftrightarrow & 189x+72x& = & 7+42 \\\Leftrightarrow & \color{red}{261} x& = & 49 \\\Leftrightarrow & x = \frac{49}{261} & & \\ & V = \left\{ \frac{49}{261} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{4}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-44} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -594x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & -594x+693x& = & 45+44 \\\Leftrightarrow & \color{red}{99} x& = & 89 \\\Leftrightarrow & x = \frac{89}{99} & & \\ & V = \left\{ \frac{89}{99} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 24x-\frac{12}{11}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-60} & = & \color{red}{275x} +33 \\\Leftrightarrow & 1320x \color{red}{-60} \color{blue}{+60} \color{blue}{-275x} & = & \color{red}{275x} +33 \color{blue}{-275x} \color{blue}{+60} \\\Leftrightarrow & 1320x-275x& = & 33+60 \\\Leftrightarrow & \color{red}{1045} x& = & 93 \\\Leftrightarrow & x = \frac{93}{1045} & & \\ & V = \left\{ \frac{93}{1045} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{18}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x- \frac{162}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{-162} & = & \color{red}{567x} +70 \\\Leftrightarrow & -1134x \color{red}{-162} \color{blue}{+162} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{+162} \\\Leftrightarrow & -1134x-567x& = & 70+162 \\\Leftrightarrow & \color{red}{-1701} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-1701} & & \\\Leftrightarrow & x = \frac{-232}{1701} & & \\ & V = \left\{ \frac{-232}{1701} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{63x} +24 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & 180x-63x& = & 24-8 \\\Leftrightarrow & \color{red}{117} x& = & 16 \\\Leftrightarrow & x = \frac{16}{117} & & \\ & V = \left\{ \frac{16}{117} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{385x} +45 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +45 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 990x-385x& = & 45-132 \\\Leftrightarrow & \color{red}{605} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{605} & & \\ & V = \left\{ \frac{-87}{605} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & -840x+175x& = & 42+150 \\\Leftrightarrow & \color{red}{-665} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-665} & & \\\Leftrightarrow & x = \frac{-192}{665} & & \\ & V = \left\{ \frac{-192}{665} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-16} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -140x \color{red}{-16} \color{blue}{+16} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+16} \\\Leftrightarrow & -140x+49x& = & 10+16 \\\Leftrightarrow & \color{red}{-91} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-91} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{15}{2}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+105} & = & \color{red}{98x} +4 \\\Leftrightarrow & 168x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +4 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & 168x-98x& = & 4-105 \\\Leftrightarrow & \color{red}{70} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{70} & & \\ & V = \left\{ \frac{-101}{70} \right\} & \\\end{align}\)