Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{3})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{25}{3}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{175}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+175} & = & \color{red}{147x} +6 \\\Leftrightarrow & -210x \color{red}{+175} \color{blue}{-175} \color{blue}{-147x} & = & \color{red}{147x} +6 \color{blue}{-147x} \color{blue}{-175} \\\Leftrightarrow & -210x-147x& = & 6-175 \\\Leftrightarrow & \color{red}{-357} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-357} & & \\\Leftrightarrow & x = \frac{169}{357} & & \\ & V = \left\{ \frac{169}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+1)& = & 9x+\frac{3}{10} \\\Leftrightarrow & 25x-5& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{250}{ \color{blue}{10} }x- \frac{50}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 250x \color{red}{-50} & = & \color{red}{90x} +3 \\\Leftrightarrow & 250x \color{red}{-50} \color{blue}{+50} \color{blue}{-90x} & = & \color{red}{90x} +3 \color{blue}{-90x} \color{blue}{+50} \\\Leftrightarrow & 250x-90x& = & 3+50 \\\Leftrightarrow & \color{red}{160} x& = & 53 \\\Leftrightarrow & x = \frac{53}{160} & & \\ & V = \left\{ \frac{53}{160} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +70 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 70+18 \\\Leftrightarrow & \color{red}{-273} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-273} & & \\\Leftrightarrow & x = \frac{-88}{273} & & \\ & V = \left\{ \frac{-88}{273} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{8}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+88} & = & \color{red}{275x} +10 \\\Leftrightarrow & 660x \color{red}{+88} \color{blue}{-88} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{-88} \\\Leftrightarrow & 660x-275x& = & 10-88 \\\Leftrightarrow & \color{red}{385} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{385} & & \\ & V = \left\{ \frac{-78}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-18} & = & \color{red}{-55x} +10 \\\Leftrightarrow & 132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 132x+55x& = & 10+18 \\\Leftrightarrow & \color{red}{187} x& = & 28 \\\Leftrightarrow & x = \frac{28}{187} & & \\ & V = \left\{ \frac{28}{187} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{2})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -9x-\frac{9}{2}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{10}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{-63} & = & \color{red}{70x} +10 \\\Leftrightarrow & -126x \color{red}{-63} \color{blue}{+63} \color{blue}{-70x} & = & \color{red}{70x} +10 \color{blue}{-70x} \color{blue}{+63} \\\Leftrightarrow & -126x-70x& = & 10+63 \\\Leftrightarrow & \color{red}{-196} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-196} & & \\\Leftrightarrow & x = \frac{-73}{196} & & \\ & V = \left\{ \frac{-73}{196} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{3})& = & -3x+\frac{7}{5} \\\Leftrightarrow & 14x+\frac{35}{3}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x+ \frac{175}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{+175} & = & \color{red}{-45x} +21 \\\Leftrightarrow & 210x \color{red}{+175} \color{blue}{-175} \color{blue}{+45x} & = & \color{red}{-45x} +21 \color{blue}{+45x} \color{blue}{-175} \\\Leftrightarrow & 210x+45x& = & 21-175 \\\Leftrightarrow & \color{red}{255} x& = & -154 \\\Leftrightarrow & x = \frac{-154}{255} & & \\ & V = \left\{ \frac{-154}{255} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 16x+\frac{16}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+80} & = & \color{red}{135x} +24 \\\Leftrightarrow & 240x \color{red}{+80} \color{blue}{-80} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{-80} \\\Leftrightarrow & 240x-135x& = & 24-80 \\\Leftrightarrow & \color{red}{105} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{105} & & \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x-\frac{6}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-6} & = & \color{red}{77x} +2 \\\Leftrightarrow & -66x \color{red}{-6} \color{blue}{+6} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{+6} \\\Leftrightarrow & -66x-77x& = & 2+6 \\\Leftrightarrow & \color{red}{-143} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-143} & & \\\Leftrightarrow & x = \frac{-8}{143} & & \\ & V = \left\{ \frac{-8}{143} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +30 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +30 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 30+84 \\\Leftrightarrow & \color{red}{-490} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-490} & & \\\Leftrightarrow & x = \frac{-57}{245} & & \\ & V = \left\{ \frac{-57}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{224}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 224x \color{red}{-32} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 224x \color{red}{-32} \color{blue}{+32} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+32} \\\Leftrightarrow & 224x+98x& = & 21+32 \\\Leftrightarrow & \color{red}{322} x& = & 53 \\\Leftrightarrow & x = \frac{53}{322} & & \\ & V = \left\{ \frac{53}{322} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{25}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x- \frac{50}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{-50} & = & \color{red}{126x} +81 \\\Leftrightarrow & 180x \color{red}{-50} \color{blue}{+50} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{+50} \\\Leftrightarrow & 180x-126x& = & 81+50 \\\Leftrightarrow & \color{red}{54} x& = & 131 \\\Leftrightarrow & x = \frac{131}{54} & & \\ & V = \left\{ \frac{131}{54} \right\} & \\\end{align}\)