Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+60} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -168x \color{red}{+60} \color{blue}{-60} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{-60} \\\Leftrightarrow & -168x+189x& = & 56-60 \\\Leftrightarrow & \color{red}{21} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{8}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+8} & = & \color{red}{35x} +9 \\\Leftrightarrow & 84x \color{red}{+8} \color{blue}{-8} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{-8} \\\Leftrightarrow & 84x-35x& = & 9-8 \\\Leftrightarrow & \color{red}{49} x& = & 1 \\\Leftrightarrow & x = \frac{1}{49} & & \\ & V = \left\{ \frac{1}{49} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+54} \\\Leftrightarrow & -360x+75x& = & 40+54 \\\Leftrightarrow & \color{red}{-285} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-285} & & \\\Leftrightarrow & x = \frac{-94}{285} & & \\ & V = \left\{ \frac{-94}{285} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-220} & = & \color{red}{-539x} +56 \\\Leftrightarrow & 770x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & 770x+539x& = & 56+220 \\\Leftrightarrow & \color{red}{1309} x& = & 276 \\\Leftrightarrow & x = \frac{276}{1309} & & \\ & V = \left\{ \frac{276}{1309} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-125} & = & \color{red}{90x} +12 \\\Leftrightarrow & -200x \color{red}{-125} \color{blue}{+125} \color{blue}{-90x} & = & \color{red}{90x} +12 \color{blue}{-90x} \color{blue}{+125} \\\Leftrightarrow & -200x-90x& = & 12+125 \\\Leftrightarrow & \color{red}{-290} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-290} & & \\\Leftrightarrow & x = \frac{-137}{290} & & \\ & V = \left\{ \frac{-137}{290} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+20} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -140x \color{red}{+20} \color{blue}{-20} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-20} \\\Leftrightarrow & -140x+98x& = & 21-20 \\\Leftrightarrow & \color{red}{-42} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-42} & & \\\Leftrightarrow & x = \frac{-1}{42} & & \\ & V = \left\{ \frac{-1}{42} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{6}{7}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-18} & = & \color{red}{84x} +28 \\\Leftrightarrow & -315x \color{red}{-18} \color{blue}{+18} \color{blue}{-84x} & = & \color{red}{84x} +28 \color{blue}{-84x} \color{blue}{+18} \\\Leftrightarrow & -315x-84x& = & 28+18 \\\Leftrightarrow & \color{red}{-399} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-399} & & \\\Leftrightarrow & x = \frac{-46}{399} & & \\ & V = \left\{ \frac{-46}{399} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{5})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 28x+\frac{14}{5}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{980}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 980x \color{red}{+98} & = & \color{red}{-315x} +40 \\\Leftrightarrow & 980x \color{red}{+98} \color{blue}{-98} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-98} \\\Leftrightarrow & 980x+315x& = & 40-98 \\\Leftrightarrow & \color{red}{1295} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1295} & & \\ & V = \left\{ \frac{-58}{1295} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{12})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 21x-\frac{35}{12}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{42}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-35} & = & \color{red}{-48x} +42 \\\Leftrightarrow & 252x \color{red}{-35} \color{blue}{+35} \color{blue}{+48x} & = & \color{red}{-48x} +42 \color{blue}{+48x} \color{blue}{+35} \\\Leftrightarrow & 252x+48x& = & 42+35 \\\Leftrightarrow & \color{red}{300} x& = & 77 \\\Leftrightarrow & x = \frac{77}{300} & & \\ & V = \left\{ \frac{77}{300} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{3})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{25}{3}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{50}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+50} & = & \color{red}{42x} +5 \\\Leftrightarrow & 60x \color{red}{+50} \color{blue}{-50} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{-50} \\\Leftrightarrow & 60x-42x& = & 5-50 \\\Leftrightarrow & \color{red}{18} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{18} & & \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{15}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-75} & = & \color{red}{275x} +66 \\\Leftrightarrow & -660x \color{red}{-75} \color{blue}{+75} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+75} \\\Leftrightarrow & -660x-275x& = & 66+75 \\\Leftrightarrow & \color{red}{-935} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-935} & & \\\Leftrightarrow & x = \frac{-141}{935} & & \\ & V = \left\{ \frac{-141}{935} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+56} & = & \color{red}{189x} +27 \\\Leftrightarrow & 630x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & 630x-189x& = & 27-56 \\\Leftrightarrow & \color{red}{441} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{441} & & \\ & V = \left\{ \frac{-29}{441} \right\} & \\\end{align}\)