Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{24}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-48} \\\Leftrightarrow & 120x-50x& = & 45-48 \\\Leftrightarrow & \color{red}{70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -4x-\frac{6}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{495x} +44 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{+54} \\\Leftrightarrow & -396x-495x& = & 44+54 \\\Leftrightarrow & \color{red}{-891} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-891} & & \\\Leftrightarrow & x = \frac{-98}{891} & & \\ & V = \left\{ \frac{-98}{891} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+120} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{+120} \color{blue}{-120} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-120} \\\Leftrightarrow & -336x-140x& = & 63-120 \\\Leftrightarrow & \color{red}{-476} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-476} & & \\\Leftrightarrow & x = \frac{57}{476} & & \\ & V = \left\{ \frac{57}{476} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -10x-\frac{15}{4}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-200}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -200x \color{red}{-75} & = & \color{red}{-140x} +36 \\\Leftrightarrow & -200x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +36 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -200x+140x& = & 36+75 \\\Leftrightarrow & \color{red}{-60} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-60} & & \\\Leftrightarrow & x = \frac{-37}{20} & & \\ & V = \left\{ \frac{-37}{20} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{20}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+100} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 900x \color{red}{+100} \color{blue}{-100} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-100} \\\Leftrightarrow & 900x+315x& = & 54-100 \\\Leftrightarrow & \color{red}{1215} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{1215} & & \\ & V = \left\{ \frac{-46}{1215} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{10})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{-770x} +50 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{+770x} & = & \color{red}{-770x} +50 \color{blue}{+770x} \color{blue}{-99} \\\Leftrightarrow & -660x+770x& = & 50-99 \\\Leftrightarrow & \color{red}{110} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{110} & & \\ & V = \left\{ \frac{-49}{110} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & 9x+\frac{5}{9} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-180} & = & \color{red}{567x} +35 \\\Leftrightarrow & 1008x \color{red}{-180} \color{blue}{+180} \color{blue}{-567x} & = & \color{red}{567x} +35 \color{blue}{-567x} \color{blue}{+180} \\\Leftrightarrow & 1008x-567x& = & 35+180 \\\Leftrightarrow & \color{red}{441} x& = & 215 \\\Leftrightarrow & x = \frac{215}{441} & & \\ & V = \left\{ \frac{215}{441} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+60} & = & \color{red}{70x} +63 \\\Leftrightarrow & 168x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 168x-70x& = & 63-60 \\\Leftrightarrow & \color{red}{98} x& = & 3 \\\Leftrightarrow & x = \frac{3}{98} & & \\ & V = \left\{ \frac{3}{98} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{270x} +9 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{-270x} & = & \color{red}{270x} +9 \color{blue}{-270x} \color{blue}{+140} \\\Leftrightarrow & 420x-270x& = & 9+140 \\\Leftrightarrow & \color{red}{150} x& = & 149 \\\Leftrightarrow & x = \frac{149}{150} & & \\ & V = \left\{ \frac{149}{150} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{4})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 14x+\frac{35}{4}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{504}{ \color{blue}{36} }x+ \frac{315}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{28}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 504x \color{red}{+315} & = & \color{red}{180x} +28 \\\Leftrightarrow & 504x \color{red}{+315} \color{blue}{-315} \color{blue}{-180x} & = & \color{red}{180x} +28 \color{blue}{-180x} \color{blue}{-315} \\\Leftrightarrow & 504x-180x& = & 28-315 \\\Leftrightarrow & \color{red}{324} x& = & -287 \\\Leftrightarrow & x = \frac{-287}{324} & & \\ & V = \left\{ \frac{-287}{324} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x- \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{-48} & = & \color{red}{-110x} +99 \\\Leftrightarrow & -528x \color{red}{-48} \color{blue}{+48} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+48} \\\Leftrightarrow & -528x+110x& = & 99+48 \\\Leftrightarrow & \color{red}{-418} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-418} & & \\\Leftrightarrow & x = \frac{-147}{418} & & \\ & V = \left\{ \frac{-147}{418} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{-40} & = & \color{red}{-112x} +35 \\\Leftrightarrow & -350x \color{red}{-40} \color{blue}{+40} \color{blue}{+112x} & = & \color{red}{-112x} +35 \color{blue}{+112x} \color{blue}{+40} \\\Leftrightarrow & -350x+112x& = & 35+40 \\\Leftrightarrow & \color{red}{-238} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-238} & & \\\Leftrightarrow & x = \frac{-75}{238} & & \\ & V = \left\{ \frac{-75}{238} \right\} & \\\end{align}\)