Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+12} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -56x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & -56x+70x& = & 35-12 \\\Leftrightarrow & \color{red}{14} x& = & 23 \\\Leftrightarrow & x = \frac{23}{14} & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{2})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-275} & = & \color{red}{44x} +4 \\\Leftrightarrow & 550x \color{red}{-275} \color{blue}{+275} \color{blue}{-44x} & = & \color{red}{44x} +4 \color{blue}{-44x} \color{blue}{+275} \\\Leftrightarrow & 550x-44x& = & 4+275 \\\Leftrightarrow & \color{red}{506} x& = & 279 \\\Leftrightarrow & x = \frac{279}{506} & & \\ & V = \left\{ \frac{279}{506} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{11})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{20}{11}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+20} & = & \color{red}{99x} +4 \\\Leftrightarrow & 176x \color{red}{+20} \color{blue}{-20} \color{blue}{-99x} & = & \color{red}{99x} +4 \color{blue}{-99x} \color{blue}{-20} \\\Leftrightarrow & 176x-99x& = & 4-20 \\\Leftrightarrow & \color{red}{77} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{77} & & \\ & V = \left\{ \frac{-16}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -4x-\frac{4}{3}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-48}{ \color{blue}{12} }x- \frac{16}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -48x \color{red}{-16} & = & \color{red}{-60x} +21 \\\Leftrightarrow & -48x \color{red}{-16} \color{blue}{+16} \color{blue}{+60x} & = & \color{red}{-60x} +21 \color{blue}{+60x} \color{blue}{+16} \\\Leftrightarrow & -48x+60x& = & 21+16 \\\Leftrightarrow & \color{red}{12} x& = & 37 \\\Leftrightarrow & x = \frac{37}{12} & & \\ & V = \left\{ \frac{37}{12} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{-18} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -264x \color{red}{-18} \color{blue}{+18} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+18} \\\Leftrightarrow & -264x+77x& = & 6+18 \\\Leftrightarrow & \color{red}{-187} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-187} & & \\\Leftrightarrow & x = \frac{-24}{187} & & \\ & V = \left\{ \frac{-24}{187} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{11})& = & -8x+\frac{9}{8} \\\Leftrightarrow & -21x+\frac{21}{11}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x+ \frac{168}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{+168} & = & \color{red}{-704x} +99 \\\Leftrightarrow & -1848x \color{red}{+168} \color{blue}{-168} \color{blue}{+704x} & = & \color{red}{-704x} +99 \color{blue}{+704x} \color{blue}{-168} \\\Leftrightarrow & -1848x+704x& = & 99-168 \\\Leftrightarrow & \color{red}{-1144} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-1144} & & \\\Leftrightarrow & x = \frac{69}{1144} & & \\ & V = \left\{ \frac{69}{1144} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{4})& = & -8x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{-352x} +40 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{+352x} & = & \color{red}{-352x} +40 \color{blue}{+352x} \color{blue}{-165} \\\Leftrightarrow & -660x+352x& = & 40-165 \\\Leftrightarrow & \color{red}{-308} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-308} & & \\\Leftrightarrow & x = \frac{125}{308} & & \\ & V = \left\{ \frac{125}{308} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+30} & = & \color{red}{275x} +44 \\\Leftrightarrow & -220x \color{red}{+30} \color{blue}{-30} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{-30} \\\Leftrightarrow & -220x-275x& = & 44-30 \\\Leftrightarrow & \color{red}{-495} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-495} & & \\\Leftrightarrow & x = \frac{-14}{495} & & \\ & V = \left\{ \frac{-14}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{12})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{25}{12}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{-125} & = & \color{red}{-420x} +72 \\\Leftrightarrow & -1200x \color{red}{-125} \color{blue}{+125} \color{blue}{+420x} & = & \color{red}{-420x} +72 \color{blue}{+420x} \color{blue}{+125} \\\Leftrightarrow & -1200x+420x& = & 72+125 \\\Leftrightarrow & \color{red}{-780} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-780} & & \\\Leftrightarrow & x = \frac{-197}{780} & & \\ & V = \left\{ \frac{-197}{780} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & -880x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -880x+385x& = & 50-132 \\\Leftrightarrow & \color{red}{-495} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-495} & & \\\Leftrightarrow & x = \frac{82}{495} & & \\ & V = \left\{ \frac{82}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{10})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{9}{10}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+18} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 240x \color{red}{+18} \color{blue}{-18} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-18} \\\Leftrightarrow & 240x+100x& = & 45-18 \\\Leftrightarrow & \color{red}{340} x& = & 27 \\\Leftrightarrow & x = \frac{27}{340} & & \\ & V = \left\{ \frac{27}{340} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{24}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{72}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+72} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -378x \color{red}{+72} \color{blue}{-72} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{-72} \\\Leftrightarrow & -378x+63x& = & 56-72 \\\Leftrightarrow & \color{red}{-315} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-315} & & \\\Leftrightarrow & x = \frac{16}{315} & & \\ & V = \left\{ \frac{16}{315} \right\} & \\\end{align}\)