Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{6}{5}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{-6} & = & \color{red}{40x} +6 \\\Leftrightarrow & 75x \color{red}{-6} \color{blue}{+6} \color{blue}{-40x} & = & \color{red}{40x} +6 \color{blue}{-40x} \color{blue}{+6} \\\Leftrightarrow & 75x-40x& = & 6+6 \\\Leftrightarrow & \color{red}{35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{35} & & \\ & V = \left\{ \frac{12}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{-21} & = & \color{red}{-40x} +9 \\\Leftrightarrow & -112x \color{red}{-21} \color{blue}{+21} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{+21} \\\Leftrightarrow & -112x+40x& = & 9+21 \\\Leftrightarrow & \color{red}{-72} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-72} & & \\\Leftrightarrow & x = \frac{-5}{12} & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{6}{11}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-42} & = & \color{red}{-693x} +33 \\\Leftrightarrow & 308x \color{red}{-42} \color{blue}{+42} \color{blue}{+693x} & = & \color{red}{-693x} +33 \color{blue}{+693x} \color{blue}{+42} \\\Leftrightarrow & 308x+693x& = & 33+42 \\\Leftrightarrow & \color{red}{1001} x& = & 75 \\\Leftrightarrow & x = \frac{75}{1001} & & \\ & V = \left\{ \frac{75}{1001} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{99x} +15 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{-99x} & = & \color{red}{99x} +15 \color{blue}{-99x} \color{blue}{-220} \\\Leftrightarrow & -264x-99x& = & 15-220 \\\Leftrightarrow & \color{red}{-363} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-363} & & \\\Leftrightarrow & x = \frac{205}{363} & & \\ & V = \left\{ \frac{205}{363} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{12})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 25x-\frac{25}{12}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-25} & = & \color{red}{48x} +16 \\\Leftrightarrow & 300x \color{red}{-25} \color{blue}{+25} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{+25} \\\Leftrightarrow & 300x-48x& = & 16+25 \\\Leftrightarrow & \color{red}{252} x& = & 41 \\\Leftrightarrow & x = \frac{41}{252} & & \\ & V = \left\{ \frac{41}{252} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & 9x+\frac{7}{3} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 9x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-60} & = & \color{red}{189x} +49 \\\Leftrightarrow & 336x \color{red}{-60} \color{blue}{+60} \color{blue}{-189x} & = & \color{red}{189x} +49 \color{blue}{-189x} \color{blue}{+60} \\\Leftrightarrow & 336x-189x& = & 49+60 \\\Leftrightarrow & \color{red}{147} x& = & 109 \\\Leftrightarrow & x = \frac{109}{147} & & \\ & V = \left\{ \frac{109}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -270x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{45} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{45} & & \\ & V = \left\{ \frac{-58}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{12}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+84} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 1540x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & 1540x+539x& = & 110-84 \\\Leftrightarrow & \color{red}{2079} x& = & 26 \\\Leftrightarrow & x = \frac{26}{2079} & & \\ & V = \left\{ \frac{26}{2079} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x+ \frac{162}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{+162} & = & \color{red}{225x} +10 \\\Leftrightarrow & 810x \color{red}{+162} \color{blue}{-162} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-162} \\\Leftrightarrow & 810x-225x& = & 10-162 \\\Leftrightarrow & \color{red}{585} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{585} & & \\ & V = \left\{ \frac{-152}{585} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{6}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+12} & = & \color{red}{70x} +21 \\\Leftrightarrow & -168x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -168x-70x& = & 21-12 \\\Leftrightarrow & \color{red}{-238} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-238} & & \\\Leftrightarrow & x = \frac{-9}{238} & & \\ & V = \left\{ \frac{-9}{238} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{+12} \\\Leftrightarrow & -90x+105x& = & 10+12 \\\Leftrightarrow & \color{red}{15} x& = & 22 \\\Leftrightarrow & x = \frac{22}{15} & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{-40} & = & \color{red}{-42x} +15 \\\Leftrightarrow & -96x \color{red}{-40} \color{blue}{+40} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{+40} \\\Leftrightarrow & -96x+42x& = & 15+40 \\\Leftrightarrow & \color{red}{-54} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-54} & & \\\Leftrightarrow & x = \frac{-55}{54} & & \\ & V = \left\{ \frac{-55}{54} \right\} & \\\end{align}\)