Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{+100} & = & \color{red}{210x} +27 \\\Leftrightarrow & -180x \color{red}{+100} \color{blue}{-100} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{-100} \\\Leftrightarrow & -180x-210x& = & 27-100 \\\Leftrightarrow & \color{red}{-390} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-390} & & \\\Leftrightarrow & x = \frac{73}{390} & & \\ & V = \left\{ \frac{73}{390} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-396}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -396x \color{red}{-48} & = & \color{red}{-308x} +99 \\\Leftrightarrow & -396x \color{red}{-48} \color{blue}{+48} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+48} \\\Leftrightarrow & -396x+308x& = & 99+48 \\\Leftrightarrow & \color{red}{-88} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-88} & & \\\Leftrightarrow & x = \frac{-147}{88} & & \\ & V = \left\{ \frac{-147}{88} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{11})& = & -6x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -6x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1375}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{+50} & = & \color{red}{-330x} +66 \\\Leftrightarrow & -1375x \color{red}{+50} \color{blue}{-50} \color{blue}{+330x} & = & \color{red}{-330x} +66 \color{blue}{+330x} \color{blue}{-50} \\\Leftrightarrow & -1375x+330x& = & 66-50 \\\Leftrightarrow & \color{red}{-1045} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-1045} & & \\\Leftrightarrow & x = \frac{-16}{1045} & & \\ & V = \left\{ \frac{-16}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 25x-\frac{15}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-165} & = & \color{red}{231x} +42 \\\Leftrightarrow & 1925x \color{red}{-165} \color{blue}{+165} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{+165} \\\Leftrightarrow & 1925x-231x& = & 42+165 \\\Leftrightarrow & \color{red}{1694} x& = & 207 \\\Leftrightarrow & x = \frac{207}{1694} & & \\ & V = \left\{ \frac{207}{1694} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -324x \color{red}{+135} & = & \color{red}{180x} +8 \\\Leftrightarrow & -324x \color{red}{+135} \color{blue}{-135} \color{blue}{-180x} & = & \color{red}{180x} +8 \color{blue}{-180x} \color{blue}{-135} \\\Leftrightarrow & -324x-180x& = & 8-135 \\\Leftrightarrow & \color{red}{-504} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-504} & & \\\Leftrightarrow & x = \frac{127}{504} & & \\ & V = \left\{ \frac{127}{504} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-35x} +9 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-24} \\\Leftrightarrow & 90x+35x& = & 9-24 \\\Leftrightarrow & \color{red}{125} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{125} & & \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-88} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -264x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & -264x+297x& = & 18+88 \\\Leftrightarrow & \color{red}{33} x& = & 106 \\\Leftrightarrow & x = \frac{106}{33} & & \\ & V = \left\{ \frac{106}{33} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{9})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{10}{9}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{20}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-20} & = & \color{red}{162x} +81 \\\Leftrightarrow & 360x \color{red}{-20} \color{blue}{+20} \color{blue}{-162x} & = & \color{red}{162x} +81 \color{blue}{-162x} \color{blue}{+20} \\\Leftrightarrow & 360x-162x& = & 81+20 \\\Leftrightarrow & \color{red}{198} x& = & 101 \\\Leftrightarrow & x = \frac{101}{198} & & \\ & V = \left\{ \frac{101}{198} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-891}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -891x \color{red}{-108} & = & \color{red}{-495x} +88 \\\Leftrightarrow & -891x \color{red}{-108} \color{blue}{+108} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{+108} \\\Leftrightarrow & -891x+495x& = & 88+108 \\\Leftrightarrow & \color{red}{-396} x& = & 196 \\\Leftrightarrow & x = \frac{196}{-396} & & \\\Leftrightarrow & x = \frac{-49}{99} & & \\ & V = \left\{ \frac{-49}{99} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 14x-\frac{14}{9}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-98} & = & \color{red}{-189x} +54 \\\Leftrightarrow & 882x \color{red}{-98} \color{blue}{+98} \color{blue}{+189x} & = & \color{red}{-189x} +54 \color{blue}{+189x} \color{blue}{+98} \\\Leftrightarrow & 882x+189x& = & 54+98 \\\Leftrightarrow & \color{red}{1071} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1071} & & \\ & V = \left\{ \frac{152}{1071} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{-200x} +15 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{+200x} & = & \color{red}{-200x} +15 \color{blue}{+200x} \color{blue}{+96} \\\Leftrightarrow & 480x+200x& = & 15+96 \\\Leftrightarrow & \color{red}{680} x& = & 111 \\\Leftrightarrow & x = \frac{111}{680} & & \\ & V = \left\{ \frac{111}{680} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -21x-\frac{14}{9}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-14} & = & \color{red}{-72x} +30 \\\Leftrightarrow & -189x \color{red}{-14} \color{blue}{+14} \color{blue}{+72x} & = & \color{red}{-72x} +30 \color{blue}{+72x} \color{blue}{+14} \\\Leftrightarrow & -189x+72x& = & 30+14 \\\Leftrightarrow & \color{red}{-117} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-117} & & \\\Leftrightarrow & x = \frac{-44}{117} & & \\ & V = \left\{ \frac{-44}{117} \right\} & \\\end{align}\)