Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+72} & = & \color{red}{308x} +99 \\\Leftrightarrow & -1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & -1320x-308x& = & 99-72 \\\Leftrightarrow & \color{red}{-1628} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-1628} & & \\\Leftrightarrow & x = \frac{-27}{1628} & & \\ & V = \left\{ \frac{-27}{1628} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 4x-\frac{6}{11}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-42} & = & \color{red}{539x} +66 \\\Leftrightarrow & 308x \color{red}{-42} \color{blue}{+42} \color{blue}{-539x} & = & \color{red}{539x} +66 \color{blue}{-539x} \color{blue}{+42} \\\Leftrightarrow & 308x-539x& = & 66+42 \\\Leftrightarrow & \color{red}{-231} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-231} & & \\\Leftrightarrow & x = \frac{-36}{77} & & \\ & V = \left\{ \frac{-36}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{15}{8}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+45} & = & \color{red}{168x} +64 \\\Leftrightarrow & -240x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +64 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & -240x-168x& = & 64-45 \\\Leftrightarrow & \color{red}{-408} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-408} & & \\\Leftrightarrow & x = \frac{-19}{408} & & \\ & V = \left\{ \frac{-19}{408} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{10})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{9}{10}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{-27} & = & \color{red}{-210x} +40 \\\Leftrightarrow & 450x \color{red}{-27} \color{blue}{+27} \color{blue}{+210x} & = & \color{red}{-210x} +40 \color{blue}{+210x} \color{blue}{+27} \\\Leftrightarrow & 450x+210x& = & 40+27 \\\Leftrightarrow & \color{red}{660} x& = & 67 \\\Leftrightarrow & x = \frac{67}{660} & & \\ & V = \left\{ \frac{67}{660} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & -3x+\frac{5}{3} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -3x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+14} & = & \color{red}{-9x} +5 \\\Leftrightarrow & 42x \color{red}{+14} \color{blue}{-14} \color{blue}{+9x} & = & \color{red}{-9x} +5 \color{blue}{+9x} \color{blue}{-14} \\\Leftrightarrow & 42x+9x& = & 5-14 \\\Leftrightarrow & \color{red}{51} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{51} & & \\\Leftrightarrow & x = \frac{-3}{17} & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+64} & = & \color{red}{-252x} +63 \\\Leftrightarrow & 224x \color{red}{+64} \color{blue}{-64} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{-64} \\\Leftrightarrow & 224x+252x& = & 63-64 \\\Leftrightarrow & \color{red}{476} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{476} & & \\ & V = \left\{ \frac{-1}{476} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 4x+\frac{2}{9} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{180}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 405x \color{red}{-108} & = & \color{red}{180x} +10 \\\Leftrightarrow & 405x \color{red}{-108} \color{blue}{+108} \color{blue}{-180x} & = & \color{red}{180x} +10 \color{blue}{-180x} \color{blue}{+108} \\\Leftrightarrow & 405x-180x& = & 10+108 \\\Leftrightarrow & \color{red}{225} x& = & 118 \\\Leftrightarrow & x = \frac{118}{225} & & \\ & V = \left\{ \frac{118}{225} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-96} & = & \color{red}{440x} +55 \\\Leftrightarrow & -1056x \color{red}{-96} \color{blue}{+96} \color{blue}{-440x} & = & \color{red}{440x} +55 \color{blue}{-440x} \color{blue}{+96} \\\Leftrightarrow & -1056x-440x& = & 55+96 \\\Leftrightarrow & \color{red}{-1496} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-1496} & & \\\Leftrightarrow & x = \frac{-151}{1496} & & \\ & V = \left\{ \frac{-151}{1496} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+20} & = & \color{red}{126x} +35 \\\Leftrightarrow & -56x \color{red}{+20} \color{blue}{-20} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-20} \\\Leftrightarrow & -56x-126x& = & 35-20 \\\Leftrightarrow & \color{red}{-182} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-182} & & \\\Leftrightarrow & x = \frac{-15}{182} & & \\ & V = \left\{ \frac{-15}{182} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{6})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{25}{6}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+25} & = & \color{red}{-24x} +8 \\\Leftrightarrow & -90x \color{red}{+25} \color{blue}{-25} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{-25} \\\Leftrightarrow & -90x+24x& = & 8-25 \\\Leftrightarrow & \color{red}{-66} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-66} & & \\\Leftrightarrow & x = \frac{17}{66} & & \\ & V = \left\{ \frac{17}{66} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{-245} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-245} & & \\\Leftrightarrow & x = \frac{-99}{245} & & \\ & V = \left\{ \frac{-99}{245} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{9})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{4}{9}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-28} & = & \color{red}{-441x} +81 \\\Leftrightarrow & -630x \color{red}{-28} \color{blue}{+28} \color{blue}{+441x} & = & \color{red}{-441x} +81 \color{blue}{+441x} \color{blue}{+28} \\\Leftrightarrow & -630x+441x& = & 81+28 \\\Leftrightarrow & \color{red}{-189} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-189} & & \\\Leftrightarrow & x = \frac{-109}{189} & & \\ & V = \left\{ \frac{-109}{189} \right\} & \\\end{align}\)