Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-66} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -770x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -770x+539x& = & 70+66 \\\Leftrightarrow & \color{red}{-231} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-231} & & \\\Leftrightarrow & x = \frac{-136}{231} & & \\ & V = \left\{ \frac{-136}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{11})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -21x-\frac{28}{11}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2310}{ \color{blue}{110} }x- \frac{280}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2310x \color{red}{-280} & = & \color{red}{-880x} +99 \\\Leftrightarrow & -2310x \color{red}{-280} \color{blue}{+280} \color{blue}{+880x} & = & \color{red}{-880x} +99 \color{blue}{+880x} \color{blue}{+280} \\\Leftrightarrow & -2310x+880x& = & 99+280 \\\Leftrightarrow & \color{red}{-1430} x& = & 379 \\\Leftrightarrow & x = \frac{379}{-1430} & & \\\Leftrightarrow & x = \frac{-379}{1430} & & \\ & V = \left\{ \frac{-379}{1430} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{20}{3}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{-20} & = & \color{red}{12x} +2 \\\Leftrightarrow & -45x \color{red}{-20} \color{blue}{+20} \color{blue}{-12x} & = & \color{red}{12x} +2 \color{blue}{-12x} \color{blue}{+20} \\\Leftrightarrow & -45x-12x& = & 2+20 \\\Leftrightarrow & \color{red}{-57} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-57} & & \\\Leftrightarrow & x = \frac{-22}{57} & & \\ & V = \left\{ \frac{-22}{57} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{6}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{36}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{+36} \\\Leftrightarrow & -360x+150x& = & 25+36 \\\Leftrightarrow & \color{red}{-210} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-210} & & \\\Leftrightarrow & x = \frac{-61}{210} & & \\ & V = \left\{ \frac{-61}{210} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{5})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-4} & = & \color{red}{25x} +9 \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-25x} & = & \color{red}{25x} +9 \color{blue}{-25x} \color{blue}{+4} \\\Leftrightarrow & 20x-25x& = & 9+4 \\\Leftrightarrow & \color{red}{-5} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-5} & & \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{2})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 6x+\frac{9}{2}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{+54} & = & \color{red}{84x} +7 \\\Leftrightarrow & 72x \color{red}{+54} \color{blue}{-54} \color{blue}{-84x} & = & \color{red}{84x} +7 \color{blue}{-84x} \color{blue}{-54} \\\Leftrightarrow & 72x-84x& = & 7-54 \\\Leftrightarrow & \color{red}{-12} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-12} & & \\\Leftrightarrow & x = \frac{47}{12} & & \\ & V = \left\{ \frac{47}{12} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+40} & = & \color{red}{105x} +24 \\\Leftrightarrow & -240x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & -240x-105x& = & 24-40 \\\Leftrightarrow & \color{red}{-345} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-345} & & \\\Leftrightarrow & x = \frac{16}{345} & & \\ & V = \left\{ \frac{16}{345} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{6})& = & -2x+\frac{7}{5} \\\Leftrightarrow & 21x-\frac{35}{6}& = & -2x+\frac{7}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-60}{ \color{blue}{30} }x+ \frac{42}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{-60x} +42 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{+60x} & = & \color{red}{-60x} +42 \color{blue}{+60x} \color{blue}{+175} \\\Leftrightarrow & 630x+60x& = & 42+175 \\\Leftrightarrow & \color{red}{690} x& = & 217 \\\Leftrightarrow & x = \frac{217}{690} & & \\ & V = \left\{ \frac{217}{690} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -16x-\frac{8}{9}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-576}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -576x \color{red}{-32} & = & \color{red}{252x} +81 \\\Leftrightarrow & -576x \color{red}{-32} \color{blue}{+32} \color{blue}{-252x} & = & \color{red}{252x} +81 \color{blue}{-252x} \color{blue}{+32} \\\Leftrightarrow & -576x-252x& = & 81+32 \\\Leftrightarrow & \color{red}{-828} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-828} & & \\\Leftrightarrow & x = \frac{-113}{828} & & \\ & V = \left\{ \frac{-113}{828} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{15}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+135} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 1260x \color{red}{+135} \color{blue}{-135} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{-135} \\\Leftrightarrow & 1260x+441x& = & 56-135 \\\Leftrightarrow & \color{red}{1701} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{1701} & & \\ & V = \left\{ \frac{-79}{1701} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & -8x+\frac{7}{9} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+108} & = & \color{red}{-360x} +35 \\\Leftrightarrow & -810x \color{red}{+108} \color{blue}{-108} \color{blue}{+360x} & = & \color{red}{-360x} +35 \color{blue}{+360x} \color{blue}{-108} \\\Leftrightarrow & -810x+360x& = & 35-108 \\\Leftrightarrow & \color{red}{-450} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-450} & & \\\Leftrightarrow & x = \frac{73}{450} & & \\ & V = \left\{ \frac{73}{450} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -16x-\frac{8}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-40} & = & \color{red}{-385x} +77 \\\Leftrightarrow & -880x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & -880x+385x& = & 77+40 \\\Leftrightarrow & \color{red}{-495} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-495} & & \\\Leftrightarrow & x = \frac{-13}{55} & & \\ & V = \left\{ \frac{-13}{55} \right\} & \\\end{align}\)