Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 2x+\frac{2}{7} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 2x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{-98} & = & \color{red}{42x} +6 \\\Leftrightarrow & 735x \color{red}{-98} \color{blue}{+98} \color{blue}{-42x} & = & \color{red}{42x} +6 \color{blue}{-42x} \color{blue}{+98} \\\Leftrightarrow & 735x-42x& = & 6+98 \\\Leftrightarrow & \color{red}{693} x& = & 104 \\\Leftrightarrow & x = \frac{104}{693} & & \\ & V = \left\{ \frac{104}{693} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 990x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{715} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{715} & & \\ & V = \left\{ \frac{-107}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{-12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 80x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 80x+25x& = & 4+12 \\\Leftrightarrow & \color{red}{105} x& = & 16 \\\Leftrightarrow & x = \frac{16}{105} & & \\ & V = \left\{ \frac{16}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+264} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -1320x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & -1320x+275x& = & 30-264 \\\Leftrightarrow & \color{red}{-1045} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{-1045} & & \\\Leftrightarrow & x = \frac{234}{1045} & & \\ & V = \left\{ \frac{234}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{28}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x+ \frac{140}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{+140} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 1155x \color{red}{+140} \color{blue}{-140} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-140} \\\Leftrightarrow & 1155x+275x& = & 66-140 \\\Leftrightarrow & \color{red}{1430} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1430} & & \\\Leftrightarrow & x = \frac{-37}{715} & & \\ & V = \left\{ \frac{-37}{715} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-84} & = & \color{red}{315x} +10 \\\Leftrightarrow & -700x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & -700x-315x& = & 10+84 \\\Leftrightarrow & \color{red}{-1015} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-1015} & & \\\Leftrightarrow & x = \frac{-94}{1015} & & \\ & V = \left\{ \frac{-94}{1015} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-50}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -50x \color{red}{-6} & = & \color{red}{35x} +6 \\\Leftrightarrow & -50x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -50x-35x& = & 6+6 \\\Leftrightarrow & \color{red}{-85} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-85} & & \\\Leftrightarrow & x = \frac{-12}{85} & & \\ & V = \left\{ \frac{-12}{85} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +28 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 28-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1001} & & \\\Leftrightarrow & x = \frac{38}{1001} & & \\ & V = \left\{ \frac{38}{1001} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{8}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{105x} +10 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-24} \\\Leftrightarrow & -90x-105x& = & 10-24 \\\Leftrightarrow & \color{red}{-195} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-195} & & \\\Leftrightarrow & x = \frac{14}{195} & & \\ & V = \left\{ \frac{14}{195} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & 75x+35x& = & 4-12 \\\Leftrightarrow & \color{red}{110} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{110} & & \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{12}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-36} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 336x \color{red}{-36} \color{blue}{+36} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{+36} \\\Leftrightarrow & 336x+63x& = & 14+36 \\\Leftrightarrow & \color{red}{399} x& = & 50 \\\Leftrightarrow & x = \frac{50}{399} & & \\ & V = \left\{ \frac{50}{399} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{11})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{16}{11}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-16} & = & \color{red}{99x} +6 \\\Leftrightarrow & 88x \color{red}{-16} \color{blue}{+16} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{+16} \\\Leftrightarrow & 88x-99x& = & 6+16 \\\Leftrightarrow & \color{red}{-11} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-11} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)