Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & 378x+147x& = & 70+90 \\\Leftrightarrow & \color{red}{525} x& = & 160 \\\Leftrightarrow & x = \frac{160}{525} & & \\\Leftrightarrow & x = \frac{32}{105} & & \\ & V = \left\{ \frac{32}{105} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{+105} & = & \color{red}{224x} +80 \\\Leftrightarrow & -840x \color{red}{+105} \color{blue}{-105} \color{blue}{-224x} & = & \color{red}{224x} +80 \color{blue}{-224x} \color{blue}{-105} \\\Leftrightarrow & -840x-224x& = & 80-105 \\\Leftrightarrow & \color{red}{-1064} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-1064} & & \\\Leftrightarrow & x = \frac{25}{1064} & & \\ & V = \left\{ \frac{25}{1064} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+24} & = & \color{red}{-45x} +10 \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-24} \\\Leftrightarrow & -36x+45x& = & 10-24 \\\Leftrightarrow & \color{red}{9} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{+16} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 96x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & 96x+42x& = & 21-16 \\\Leftrightarrow & \color{red}{138} x& = & 5 \\\Leftrightarrow & x = \frac{5}{138} & & \\ & V = \left\{ \frac{5}{138} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{7})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{15}{7}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+15} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 84x \color{red}{+15} \color{blue}{-15} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-15} \\\Leftrightarrow & 84x+35x& = & 4-15 \\\Leftrightarrow & \color{red}{119} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{119} & & \\ & V = \left\{ \frac{-11}{119} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & 2x+\frac{6}{11} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-220} & = & \color{red}{66x} +18 \\\Leftrightarrow & -825x \color{red}{-220} \color{blue}{+220} \color{blue}{-66x} & = & \color{red}{66x} +18 \color{blue}{-66x} \color{blue}{+220} \\\Leftrightarrow & -825x-66x& = & 18+220 \\\Leftrightarrow & \color{red}{-891} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-891} & & \\\Leftrightarrow & x = \frac{-238}{891} & & \\ & V = \left\{ \frac{-238}{891} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-16} & = & \color{red}{-162x} +81 \\\Leftrightarrow & -144x \color{red}{-16} \color{blue}{+16} \color{blue}{+162x} & = & \color{red}{-162x} +81 \color{blue}{+162x} \color{blue}{+16} \\\Leftrightarrow & -144x+162x& = & 81+16 \\\Leftrightarrow & \color{red}{18} x& = & 97 \\\Leftrightarrow & x = \frac{97}{18} & & \\ & V = \left\{ \frac{97}{18} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -210x+245x& = & 42-30 \\\Leftrightarrow & \color{red}{35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{35} & & \\ & V = \left\{ \frac{12}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & 8x+\frac{9}{7} \\\Leftrightarrow & -15x+\frac{6}{11}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+42} & = & \color{red}{616x} +99 \\\Leftrightarrow & -1155x \color{red}{+42} \color{blue}{-42} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{-42} \\\Leftrightarrow & -1155x-616x& = & 99-42 \\\Leftrightarrow & \color{red}{-1771} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-1771} & & \\\Leftrightarrow & x = \frac{-57}{1771} & & \\ & V = \left\{ \frac{-57}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-66} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 462x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 462x+385x& = & 14+66 \\\Leftrightarrow & \color{red}{847} x& = & 80 \\\Leftrightarrow & x = \frac{80}{847} & & \\ & V = \left\{ \frac{80}{847} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-42} & = & \color{red}{245x} +45 \\\Leftrightarrow & 140x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & 140x-245x& = & 45+42 \\\Leftrightarrow & \color{red}{-105} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-105} & & \\\Leftrightarrow & x = \frac{-29}{35} & & \\ & V = \left\{ \frac{-29}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{3})& = & 4x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{25}{3}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{275}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-275} & = & \color{red}{132x} +15 \\\Leftrightarrow & -495x \color{red}{-275} \color{blue}{+275} \color{blue}{-132x} & = & \color{red}{132x} +15 \color{blue}{-132x} \color{blue}{+275} \\\Leftrightarrow & -495x-132x& = & 15+275 \\\Leftrightarrow & \color{red}{-627} x& = & 290 \\\Leftrightarrow & x = \frac{290}{-627} & & \\\Leftrightarrow & x = \frac{-290}{627} & & \\ & V = \left\{ \frac{-290}{627} \right\} & \\\end{align}\)