Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -20x-\frac{16}{3}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-112} & = & \color{red}{63x} +9 \\\Leftrightarrow & -420x \color{red}{-112} \color{blue}{+112} \color{blue}{-63x} & = & \color{red}{63x} +9 \color{blue}{-63x} \color{blue}{+112} \\\Leftrightarrow & -420x-63x& = & 9+112 \\\Leftrightarrow & \color{red}{-483} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-483} & & \\\Leftrightarrow & x = \frac{-121}{483} & & \\ & V = \left\{ \frac{-121}{483} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{8}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-24} & = & \color{red}{189x} +28 \\\Leftrightarrow & -420x \color{red}{-24} \color{blue}{+24} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+24} \\\Leftrightarrow & -420x-189x& = & 28+24 \\\Leftrightarrow & \color{red}{-609} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-609} & & \\\Leftrightarrow & x = \frac{-52}{609} & & \\ & V = \left\{ \frac{-52}{609} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 12x+\frac{16}{7}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+80} & = & \color{red}{175x} +63 \\\Leftrightarrow & 420x \color{red}{+80} \color{blue}{-80} \color{blue}{-175x} & = & \color{red}{175x} +63 \color{blue}{-175x} \color{blue}{-80} \\\Leftrightarrow & 420x-175x& = & 63-80 \\\Leftrightarrow & \color{red}{245} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{245} & & \\ & V = \left\{ \frac{-17}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+45} & = & \color{red}{-168x} +64 \\\Leftrightarrow & -480x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +64 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & -480x+168x& = & 64-45 \\\Leftrightarrow & \color{red}{-312} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-312} & & \\\Leftrightarrow & x = \frac{-19}{312} & & \\ & V = \left\{ \frac{-19}{312} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{24}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+168} & = & \color{red}{175x} +15 \\\Leftrightarrow & -420x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & -420x-175x& = & 15-168 \\\Leftrightarrow & \color{red}{-595} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-595} & & \\\Leftrightarrow & x = \frac{9}{35} & & \\ & V = \left\{ \frac{9}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{135x} +18 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & 360x-135x& = & 18+40 \\\Leftrightarrow & \color{red}{225} x& = & 58 \\\Leftrightarrow & x = \frac{58}{225} & & \\ & V = \left\{ \frac{58}{225} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{11})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{14}{11}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{28}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-28} & = & \color{red}{176x} +55 \\\Leftrightarrow & -462x \color{red}{-28} \color{blue}{+28} \color{blue}{-176x} & = & \color{red}{176x} +55 \color{blue}{-176x} \color{blue}{+28} \\\Leftrightarrow & -462x-176x& = & 55+28 \\\Leftrightarrow & \color{red}{-638} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-638} & & \\\Leftrightarrow & x = \frac{-83}{638} & & \\ & V = \left\{ \frac{-83}{638} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-42} & = & \color{red}{245x} +20 \\\Leftrightarrow & -350x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & -350x-245x& = & 20+42 \\\Leftrightarrow & \color{red}{-595} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-595} & & \\\Leftrightarrow & x = \frac{-62}{595} & & \\ & V = \left\{ \frac{-62}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-20} & = & \color{red}{63x} +30 \\\Leftrightarrow & -180x \color{red}{-20} \color{blue}{+20} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+20} \\\Leftrightarrow & -180x-63x& = & 30+20 \\\Leftrightarrow & \color{red}{-243} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-243} & & \\\Leftrightarrow & x = \frac{-50}{243} & & \\ & V = \left\{ \frac{-50}{243} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{7})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-6} & = & \color{red}{21x} +10 \\\Leftrightarrow & 70x \color{red}{-6} \color{blue}{+6} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+6} \\\Leftrightarrow & 70x-21x& = & 10+6 \\\Leftrightarrow & \color{red}{49} x& = & 16 \\\Leftrightarrow & x = \frac{16}{49} & & \\ & V = \left\{ \frac{16}{49} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{1}{3})& = & -9x+\frac{7}{10} \\\Leftrightarrow & -35x+\frac{7}{3}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{+70} & = & \color{red}{-270x} +21 \\\Leftrightarrow & -1050x \color{red}{+70} \color{blue}{-70} \color{blue}{+270x} & = & \color{red}{-270x} +21 \color{blue}{+270x} \color{blue}{-70} \\\Leftrightarrow & -1050x+270x& = & 21-70 \\\Leftrightarrow & \color{red}{-780} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-780} & & \\\Leftrightarrow & x = \frac{49}{780} & & \\ & V = \left\{ \frac{49}{780} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-96} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 1200x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 1200x+280x& = & 35+96 \\\Leftrightarrow & \color{red}{1480} x& = & 131 \\\Leftrightarrow & x = \frac{131}{1480} & & \\ & V = \left\{ \frac{131}{1480} \right\} & \\\end{align}\)