Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{9})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{16}{9}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x+ \frac{64}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{+64} & = & \color{red}{-252x} +21 \\\Leftrightarrow & 432x \color{red}{+64} \color{blue}{-64} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-64} \\\Leftrightarrow & 432x+252x& = & 21-64 \\\Leftrightarrow & \color{red}{684} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{684} & & \\ & V = \left\{ \frac{-43}{684} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1008}{ \color{blue}{84} }x- \frac{240}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1008x \color{red}{-240} & = & \color{red}{420x} +49 \\\Leftrightarrow & -1008x \color{red}{-240} \color{blue}{+240} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{+240} \\\Leftrightarrow & -1008x-420x& = & 49+240 \\\Leftrightarrow & \color{red}{-1428} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-1428} & & \\\Leftrightarrow & x = \frac{-17}{84} & & \\ & V = \left\{ \frac{-17}{84} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-10x} +2 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+10x} & = & \color{red}{-10x} +2 \color{blue}{+10x} \color{blue}{-12} \\\Leftrightarrow & 75x+10x& = & 2-12 \\\Leftrightarrow & \color{red}{85} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{85} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{-405x} +36 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{+405x} & = & \color{red}{-405x} +36 \color{blue}{+405x} \color{blue}{-20} \\\Leftrightarrow & 180x+405x& = & 36-20 \\\Leftrightarrow & \color{red}{585} x& = & 16 \\\Leftrightarrow & x = \frac{16}{585} & & \\ & V = \left\{ \frac{16}{585} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{-49x} +8 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -70x+49x& = & 8+10 \\\Leftrightarrow & \color{red}{-21} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-21} & & \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x-\frac{20}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{60}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-60} & = & \color{red}{231x} +22 \\\Leftrightarrow & -528x \color{red}{-60} \color{blue}{+60} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+60} \\\Leftrightarrow & -528x-231x& = & 22+60 \\\Leftrightarrow & \color{red}{-759} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-759} & & \\\Leftrightarrow & x = \frac{-82}{759} & & \\ & V = \left\{ \frac{-82}{759} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{7})& = & -4x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{20}{7}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+180} & = & \color{red}{-252x} +14 \\\Leftrightarrow & -945x \color{red}{+180} \color{blue}{-180} \color{blue}{+252x} & = & \color{red}{-252x} +14 \color{blue}{+252x} \color{blue}{-180} \\\Leftrightarrow & -945x+252x& = & 14-180 \\\Leftrightarrow & \color{red}{-693} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-693} & & \\\Leftrightarrow & x = \frac{166}{693} & & \\ & V = \left\{ \frac{166}{693} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+180} & = & \color{red}{315x} +70 \\\Leftrightarrow & -1575x \color{red}{+180} \color{blue}{-180} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{-180} \\\Leftrightarrow & -1575x-315x& = & 70-180 \\\Leftrightarrow & \color{red}{-1890} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{-1890} & & \\\Leftrightarrow & x = \frac{11}{189} & & \\ & V = \left\{ \frac{11}{189} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{6}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{-24} & = & \color{red}{-220x} +99 \\\Leftrightarrow & -528x \color{red}{-24} \color{blue}{+24} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+24} \\\Leftrightarrow & -528x+220x& = & 99+24 \\\Leftrightarrow & \color{red}{-308} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-308} & & \\\Leftrightarrow & x = \frac{-123}{308} & & \\ & V = \left\{ \frac{-123}{308} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & -2x+\frac{8}{5} \\\Leftrightarrow & -28x-\frac{35}{9}& = & -2x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-175} & = & \color{red}{-90x} +72 \\\Leftrightarrow & -1260x \color{red}{-175} \color{blue}{+175} \color{blue}{+90x} & = & \color{red}{-90x} +72 \color{blue}{+90x} \color{blue}{+175} \\\Leftrightarrow & -1260x+90x& = & 72+175 \\\Leftrightarrow & \color{red}{-1170} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-1170} & & \\\Leftrightarrow & x = \frac{-19}{90} & & \\ & V = \left\{ \frac{-19}{90} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-35} \\\Leftrightarrow & -126x+45x& = & 6-35 \\\Leftrightarrow & \color{red}{-81} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-81} & & \\\Leftrightarrow & x = \frac{29}{81} & & \\ & V = \left\{ \frac{29}{81} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-32} & = & \color{red}{70x} +49 \\\Leftrightarrow & -168x \color{red}{-32} \color{blue}{+32} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{+32} \\\Leftrightarrow & -168x-70x& = & 49+32 \\\Leftrightarrow & \color{red}{-238} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-238} & & \\\Leftrightarrow & x = \frac{-81}{238} & & \\ & V = \left\{ \frac{-81}{238} \right\} & \\\end{align}\)