Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-840}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -840x \color{red}{-120} & = & \color{red}{-196x} +35 \\\Leftrightarrow & -840x \color{red}{-120} \color{blue}{+120} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{+120} \\\Leftrightarrow & -840x+196x& = & 35+120 \\\Leftrightarrow & \color{red}{-644} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-644} & & \\\Leftrightarrow & x = \frac{-155}{644} & & \\ & V = \left\{ \frac{-155}{644} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & -2x+\frac{3}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -2x+\frac{3}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-176}{ \color{blue}{88} }x+ \frac{24}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-176x} +24 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +24 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & 1320x+176x& = & 24-165 \\\Leftrightarrow & \color{red}{1496} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{1496} & & \\ & V = \left\{ \frac{-141}{1496} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{5}{12} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-480}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -480x \color{red}{+144} & = & \color{red}{-540x} +25 \\\Leftrightarrow & -480x \color{red}{+144} \color{blue}{-144} \color{blue}{+540x} & = & \color{red}{-540x} +25 \color{blue}{+540x} \color{blue}{-144} \\\Leftrightarrow & -480x+540x& = & 25-144 \\\Leftrightarrow & \color{red}{60} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{60} & & \\ & V = \left\{ \frac{-119}{60} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{4}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+4} & = & \color{red}{63x} +30 \\\Leftrightarrow & 90x \color{red}{+4} \color{blue}{-4} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-4} \\\Leftrightarrow & 90x-63x& = & 30-4 \\\Leftrightarrow & \color{red}{27} x& = & 26 \\\Leftrightarrow & x = \frac{26}{27} & & \\ & V = \left\{ \frac{26}{27} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{6})& = & 2x+\frac{4}{11} \\\Leftrightarrow & 35x+\frac{35}{6}& = & 2x+\frac{4}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{2310}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{132}{ \color{blue}{66} }x+ \frac{24}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 2310x \color{red}{+385} & = & \color{red}{132x} +24 \\\Leftrightarrow & 2310x \color{red}{+385} \color{blue}{-385} \color{blue}{-132x} & = & \color{red}{132x} +24 \color{blue}{-132x} \color{blue}{-385} \\\Leftrightarrow & 2310x-132x& = & 24-385 \\\Leftrightarrow & \color{red}{2178} x& = & -361 \\\Leftrightarrow & x = \frac{-361}{2178} & & \\ & V = \left\{ \frac{-361}{2178} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{25x} +2 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 60x-25x& = & 2+12 \\\Leftrightarrow & \color{red}{35} x& = & 14 \\\Leftrightarrow & x = \frac{14}{35} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1980}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1980x \color{red}{-108} & = & \color{red}{462x} +55 \\\Leftrightarrow & -1980x \color{red}{-108} \color{blue}{+108} \color{blue}{-462x} & = & \color{red}{462x} +55 \color{blue}{-462x} \color{blue}{+108} \\\Leftrightarrow & -1980x-462x& = & 55+108 \\\Leftrightarrow & \color{red}{-2442} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-2442} & & \\\Leftrightarrow & x = \frac{-163}{2442} & & \\ & V = \left\{ \frac{-163}{2442} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{8})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{15}{8}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{280x} +48 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{-280x} & = & \color{red}{280x} +48 \color{blue}{-280x} \color{blue}{+75} \\\Leftrightarrow & -240x-280x& = & 48+75 \\\Leftrightarrow & \color{red}{-520} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-520} & & \\\Leftrightarrow & x = \frac{-123}{520} & & \\ & V = \left\{ \frac{-123}{520} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{35x} +9 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -80x-35x& = & 9+12 \\\Leftrightarrow & \color{red}{-115} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-115} & & \\\Leftrightarrow & x = \frac{-21}{115} & & \\ & V = \left\{ \frac{-21}{115} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+20} & = & \color{red}{-27x} +8 \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-20} \\\Leftrightarrow & -24x+27x& = & 8-20 \\\Leftrightarrow & \color{red}{3} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{3} & & \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{9}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-9} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -84x \color{red}{-9} \color{blue}{+9} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+9} \\\Leftrightarrow & -84x+35x& = & 2+9 \\\Leftrightarrow & \color{red}{-49} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-49} & & \\\Leftrightarrow & x = \frac{-11}{49} & & \\ & V = \left\{ \frac{-11}{49} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{2})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{25}{2}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+275} & = & \color{red}{176x} +20 \\\Leftrightarrow & -330x \color{red}{+275} \color{blue}{-275} \color{blue}{-176x} & = & \color{red}{176x} +20 \color{blue}{-176x} \color{blue}{-275} \\\Leftrightarrow & -330x-176x& = & 20-275 \\\Leftrightarrow & \color{red}{-506} x& = & -255 \\\Leftrightarrow & x = \frac{-255}{-506} & & \\\Leftrightarrow & x = \frac{255}{506} & & \\ & V = \left\{ \frac{255}{506} \right\} & \\\end{align}\)