Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 270x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{345} x& = & 14 \\\Leftrightarrow & x = \frac{14}{345} & & \\ & V = \left\{ \frac{14}{345} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{11})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -14x+\frac{21}{11}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x+ \frac{168}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{+168} & = & \color{red}{264x} +77 \\\Leftrightarrow & -1232x \color{red}{+168} \color{blue}{-168} \color{blue}{-264x} & = & \color{red}{264x} +77 \color{blue}{-264x} \color{blue}{-168} \\\Leftrightarrow & -1232x-264x& = & 77-168 \\\Leftrightarrow & \color{red}{-1496} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{-1496} & & \\\Leftrightarrow & x = \frac{91}{1496} & & \\ & V = \left\{ \frac{91}{1496} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+70} & = & \color{red}{539x} +99 \\\Leftrightarrow & -770x \color{red}{+70} \color{blue}{-70} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-70} \\\Leftrightarrow & -770x-539x& = & 99-70 \\\Leftrightarrow & \color{red}{-1309} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-1309} & & \\\Leftrightarrow & x = \frac{-29}{1309} & & \\ & V = \left\{ \frac{-29}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{11})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -8x-\frac{8}{11}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-880}{ \color{blue}{110} }x- \frac{80}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -880x \color{red}{-80} & = & \color{red}{990x} +99 \\\Leftrightarrow & -880x \color{red}{-80} \color{blue}{+80} \color{blue}{-990x} & = & \color{red}{990x} +99 \color{blue}{-990x} \color{blue}{+80} \\\Leftrightarrow & -880x-990x& = & 99+80 \\\Leftrightarrow & \color{red}{-1870} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1870} & & \\\Leftrightarrow & x = \frac{-179}{1870} & & \\ & V = \left\{ \frac{-179}{1870} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+60} & = & \color{red}{27x} +4 \\\Leftrightarrow & 180x \color{red}{+60} \color{blue}{-60} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{-60} \\\Leftrightarrow & 180x-27x& = & 4-60 \\\Leftrightarrow & \color{red}{153} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{153} & & \\ & V = \left\{ \frac{-56}{153} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-16} & = & \color{red}{35x} +4 \\\Leftrightarrow & 84x \color{red}{-16} \color{blue}{+16} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+16} \\\Leftrightarrow & 84x-35x& = & 4+16 \\\Leftrightarrow & \color{red}{49} x& = & 20 \\\Leftrightarrow & x = \frac{20}{49} & & \\ & V = \left\{ \frac{20}{49} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{21}{8}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{-63} & = & \color{red}{120x} +32 \\\Leftrightarrow & -672x \color{red}{-63} \color{blue}{+63} \color{blue}{-120x} & = & \color{red}{120x} +32 \color{blue}{-120x} \color{blue}{+63} \\\Leftrightarrow & -672x-120x& = & 32+63 \\\Leftrightarrow & \color{red}{-792} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-792} & & \\\Leftrightarrow & x = \frac{-95}{792} & & \\ & V = \left\{ \frac{-95}{792} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & -1080x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -1080x+225x& = & 40-108 \\\Leftrightarrow & \color{red}{-855} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-855} & & \\\Leftrightarrow & x = \frac{68}{855} & & \\ & V = \left\{ \frac{68}{855} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{3})& = & 2x+\frac{3}{7} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 2x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{-245} & = & \color{red}{42x} +9 \\\Leftrightarrow & 735x \color{red}{-245} \color{blue}{+245} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{+245} \\\Leftrightarrow & 735x-42x& = & 9+245 \\\Leftrightarrow & \color{red}{693} x& = & 254 \\\Leftrightarrow & x = \frac{254}{693} & & \\ & V = \left\{ \frac{254}{693} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{9})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{81x} +4 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{+8} \\\Leftrightarrow & 72x-81x& = & 4+8 \\\Leftrightarrow & \color{red}{-9} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-9} & & \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{7}{10} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{-60} & = & \color{red}{210x} +49 \\\Leftrightarrow & 700x \color{red}{-60} \color{blue}{+60} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{+60} \\\Leftrightarrow & 700x-210x& = & 49+60 \\\Leftrightarrow & \color{red}{490} x& = & 109 \\\Leftrightarrow & x = \frac{109}{490} & & \\ & V = \left\{ \frac{109}{490} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{168x} +30 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{-168x} & = & \color{red}{168x} +30 \color{blue}{-168x} \color{blue}{+98} \\\Leftrightarrow & -441x-168x& = & 30+98 \\\Leftrightarrow & \color{red}{-609} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-609} & & \\\Leftrightarrow & x = \frac{-128}{609} & & \\ & V = \left\{ \frac{-128}{609} \right\} & \\\end{align}\)