Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +25 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +25 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 25-36 \\\Leftrightarrow & \color{red}{255} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{255} & & \\ & V = \left\{ \frac{-11}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-66} & = & \color{red}{-440x} +30 \\\Leftrightarrow & -825x \color{red}{-66} \color{blue}{+66} \color{blue}{+440x} & = & \color{red}{-440x} +30 \color{blue}{+440x} \color{blue}{+66} \\\Leftrightarrow & -825x+440x& = & 30+66 \\\Leftrightarrow & \color{red}{-385} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-385} & & \\\Leftrightarrow & x = \frac{-96}{385} & & \\ & V = \left\{ \frac{-96}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{385x} +40 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -1650x-385x& = & 40+132 \\\Leftrightarrow & \color{red}{-2035} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-2035} & & \\\Leftrightarrow & x = \frac{-172}{2035} & & \\ & V = \left\{ \frac{-172}{2035} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & -240x+100x& = & 45-48 \\\Leftrightarrow & \color{red}{-140} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-140} & & \\\Leftrightarrow & x = \frac{3}{140} & & \\ & V = \left\{ \frac{3}{140} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-70} & = & \color{red}{45x} +12 \\\Leftrightarrow & -420x \color{red}{-70} \color{blue}{+70} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{+70} \\\Leftrightarrow & -420x-45x& = & 12+70 \\\Leftrightarrow & \color{red}{-465} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-465} & & \\\Leftrightarrow & x = \frac{-82}{465} & & \\ & V = \left\{ \frac{-82}{465} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+210} & = & \color{red}{-539x} +55 \\\Leftrightarrow & 1386x \color{red}{+210} \color{blue}{-210} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{-210} \\\Leftrightarrow & 1386x+539x& = & 55-210 \\\Leftrightarrow & \color{red}{1925} x& = & -155 \\\Leftrightarrow & x = \frac{-155}{1925} & & \\\Leftrightarrow & x = \frac{-31}{385} & & \\ & V = \left\{ \frac{-31}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & -8x+\frac{7}{6} \\\Leftrightarrow & 21x+\frac{21}{10}& = & -8x+\frac{7}{6} \\ & & & \text{kgv van noemers 10 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x+ \frac{63}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{+63} & = & \color{red}{-240x} +35 \\\Leftrightarrow & 630x \color{red}{+63} \color{blue}{-63} \color{blue}{+240x} & = & \color{red}{-240x} +35 \color{blue}{+240x} \color{blue}{-63} \\\Leftrightarrow & 630x+240x& = & 35-63 \\\Leftrightarrow & \color{red}{870} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{870} & & \\\Leftrightarrow & x = \frac{-14}{435} & & \\ & V = \left\{ \frac{-14}{435} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{11})& = & -3x+\frac{3}{11} \\\Leftrightarrow & 28x+\frac{21}{11}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{+21} & = & \color{red}{-33x} +3 \\\Leftrightarrow & 308x \color{red}{+21} \color{blue}{-21} \color{blue}{+33x} & = & \color{red}{-33x} +3 \color{blue}{+33x} \color{blue}{-21} \\\Leftrightarrow & 308x+33x& = & 3-21 \\\Leftrightarrow & \color{red}{341} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{341} & & \\ & V = \left\{ \frac{-18}{341} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{+32} & = & \color{red}{-108x} +15 \\\Leftrightarrow & -96x \color{red}{+32} \color{blue}{-32} \color{blue}{+108x} & = & \color{red}{-108x} +15 \color{blue}{+108x} \color{blue}{-32} \\\Leftrightarrow & -96x+108x& = & 15-32 \\\Leftrightarrow & \color{red}{12} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{12} & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-245x} +63 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -210x+245x& = & 63-30 \\\Leftrightarrow & \color{red}{35} x& = & 33 \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & 9x+\frac{3}{8} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{72x} +3 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +3 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & 224x-72x& = & 3+21 \\\Leftrightarrow & \color{red}{152} x& = & 24 \\\Leftrightarrow & x = \frac{24}{152} & & \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-100} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -720x \color{red}{-100} \color{blue}{+100} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+100} \\\Leftrightarrow & -720x+315x& = & 54+100 \\\Leftrightarrow & \color{red}{-405} x& = & 154 \\\Leftrightarrow & x = \frac{154}{-405} & & \\\Leftrightarrow & x = \frac{-154}{405} & & \\ & V = \left\{ \frac{-154}{405} \right\} & \\\end{align}\)