Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 50+84 \\\Leftrightarrow & \color{red}{-245} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-245} & & \\\Leftrightarrow & x = \frac{-134}{245} & & \\ & V = \left\{ \frac{-134}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{4}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+20} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -330x \color{red}{+20} \color{blue}{-20} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-20} \\\Leftrightarrow & -330x+385x& = & 22-20 \\\Leftrightarrow & \color{red}{55} x& = & 2 \\\Leftrightarrow & x = \frac{2}{55} & & \\ & V = \left\{ \frac{2}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+30} & = & \color{red}{175x} +42 \\\Leftrightarrow & -315x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & -315x-175x& = & 42-30 \\\Leftrightarrow & \color{red}{-490} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-490} & & \\\Leftrightarrow & x = \frac{-6}{245} & & \\ & V = \left\{ \frac{-6}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{12}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+60} & = & \color{red}{275x} +66 \\\Leftrightarrow & 880x \color{red}{+60} \color{blue}{-60} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-60} \\\Leftrightarrow & 880x-275x& = & 66-60 \\\Leftrightarrow & \color{red}{605} x& = & 6 \\\Leftrightarrow & x = \frac{6}{605} & & \\ & V = \left\{ \frac{6}{605} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+264} & = & \color{red}{275x} +30 \\\Leftrightarrow & 990x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & 990x-275x& = & 30-264 \\\Leftrightarrow & \color{red}{715} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{715} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{45x} +50 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-45x} & = & \color{red}{45x} +50 \color{blue}{-45x} \color{blue}{+12} \\\Leftrightarrow & 120x-45x& = & 50+12 \\\Leftrightarrow & \color{red}{75} x& = & 62 \\\Leftrightarrow & x = \frac{62}{75} & & \\ & V = \left\{ \frac{62}{75} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+60} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -90x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & -90x+63x& = & 2-60 \\\Leftrightarrow & \color{red}{-27} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-27} & & \\\Leftrightarrow & x = \frac{58}{27} & & \\ & V = \left\{ \frac{58}{27} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -6x-\frac{15}{8}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{168x} +28 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +28 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & -144x-168x& = & 28+45 \\\Leftrightarrow & \color{red}{-312} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-312} & & \\\Leftrightarrow & x = \frac{-73}{312} & & \\ & V = \left\{ \frac{-73}{312} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{11})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -14x+\frac{21}{11}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x+ \frac{105}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{+105} & = & \color{red}{-165x} +22 \\\Leftrightarrow & -770x \color{red}{+105} \color{blue}{-105} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-105} \\\Leftrightarrow & -770x+165x& = & 22-105 \\\Leftrightarrow & \color{red}{-605} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-605} & & \\\Leftrightarrow & x = \frac{83}{605} & & \\ & V = \left\{ \frac{83}{605} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{16}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{176}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-176} & = & \color{red}{385x} +50 \\\Leftrightarrow & 880x \color{red}{-176} \color{blue}{+176} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{+176} \\\Leftrightarrow & 880x-385x& = & 50+176 \\\Leftrightarrow & \color{red}{495} x& = & 226 \\\Leftrightarrow & x = \frac{226}{495} & & \\ & V = \left\{ \frac{226}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-44} & = & \color{red}{275x} +15 \\\Leftrightarrow & 330x \color{red}{-44} \color{blue}{+44} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{+44} \\\Leftrightarrow & 330x-275x& = & 15+44 \\\Leftrightarrow & \color{red}{55} x& = & 59 \\\Leftrightarrow & x = \frac{59}{55} & & \\ & V = \left\{ \frac{59}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 126x-105x& = & 56-18 \\\Leftrightarrow & \color{red}{21} x& = & 38 \\\Leftrightarrow & x = \frac{38}{21} & & \\ & V = \left\{ \frac{38}{21} \right\} & \\\end{align}\)