Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{9})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{+16} & = & \color{red}{162x} +63 \\\Leftrightarrow & -144x \color{red}{+16} \color{blue}{-16} \color{blue}{-162x} & = & \color{red}{162x} +63 \color{blue}{-162x} \color{blue}{-16} \\\Leftrightarrow & -144x-162x& = & 63-16 \\\Leftrightarrow & \color{red}{-306} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-306} & & \\\Leftrightarrow & x = \frac{-47}{306} & & \\ & V = \left\{ \frac{-47}{306} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{6}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+30} & = & \color{red}{385x} +66 \\\Leftrightarrow & -550x \color{red}{+30} \color{blue}{-30} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-30} \\\Leftrightarrow & -550x-385x& = & 66-30 \\\Leftrightarrow & \color{red}{-935} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-935} & & \\\Leftrightarrow & x = \frac{-36}{935} & & \\ & V = \left\{ \frac{-36}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{9}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+36} & = & \color{red}{-196x} +21 \\\Leftrightarrow & 336x \color{red}{+36} \color{blue}{-36} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-36} \\\Leftrightarrow & 336x+196x& = & 21-36 \\\Leftrightarrow & \color{red}{532} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{532} & & \\ & V = \left\{ \frac{-15}{532} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{5})& = & -2x+\frac{4}{7} \\\Leftrightarrow & 21x-\frac{21}{5}& = & -2x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x- \frac{147}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{-147} & = & \color{red}{-70x} +20 \\\Leftrightarrow & 735x \color{red}{-147} \color{blue}{+147} \color{blue}{+70x} & = & \color{red}{-70x} +20 \color{blue}{+70x} \color{blue}{+147} \\\Leftrightarrow & 735x+70x& = & 20+147 \\\Leftrightarrow & \color{red}{805} x& = & 167 \\\Leftrightarrow & x = \frac{167}{805} & & \\ & V = \left\{ \frac{167}{805} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{9}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{72}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-72} & = & \color{red}{-280x} +49 \\\Leftrightarrow & 672x \color{red}{-72} \color{blue}{+72} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{+72} \\\Leftrightarrow & 672x+280x& = & 49+72 \\\Leftrightarrow & \color{red}{952} x& = & 121 \\\Leftrightarrow & x = \frac{121}{952} & & \\ & V = \left\{ \frac{121}{952} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{48x} +40 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{-48x} & = & \color{red}{48x} +40 \color{blue}{-48x} \color{blue}{+45} \\\Leftrightarrow & -180x-48x& = & 40+45 \\\Leftrightarrow & \color{red}{-228} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-228} & & \\\Leftrightarrow & x = \frac{-85}{228} & & \\ & V = \left\{ \frac{-85}{228} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-32} & = & \color{red}{108x} +21 \\\Leftrightarrow & 720x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +21 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & 720x-108x& = & 21+32 \\\Leftrightarrow & \color{red}{612} x& = & 53 \\\Leftrightarrow & x = \frac{53}{612} & & \\ & V = \left\{ \frac{53}{612} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+8} & = & \color{red}{-30x} +15 \\\Leftrightarrow & 80x \color{red}{+8} \color{blue}{-8} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{-8} \\\Leftrightarrow & 80x+30x& = & 15-8 \\\Leftrightarrow & \color{red}{110} x& = & 7 \\\Leftrightarrow & x = \frac{7}{110} & & \\ & V = \left\{ \frac{7}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -21x+\frac{35}{9}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-378}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -378x \color{red}{+70} & = & \color{red}{-144x} +27 \\\Leftrightarrow & -378x \color{red}{+70} \color{blue}{-70} \color{blue}{+144x} & = & \color{red}{-144x} +27 \color{blue}{+144x} \color{blue}{-70} \\\Leftrightarrow & -378x+144x& = & 27-70 \\\Leftrightarrow & \color{red}{-234} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-234} & & \\\Leftrightarrow & x = \frac{43}{234} & & \\ & V = \left\{ \frac{43}{234} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-126} & = & \color{red}{-385x} +99 \\\Leftrightarrow & -1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & -1848x+385x& = & 99+126 \\\Leftrightarrow & \color{red}{-1463} x& = & 225 \\\Leftrightarrow & x = \frac{225}{-1463} & & \\\Leftrightarrow & x = \frac{-225}{1463} & & \\ & V = \left\{ \frac{-225}{1463} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{-12x} +8 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{+12x} & = & \color{red}{-12x} +8 \color{blue}{+12x} \color{blue}{+20} \\\Leftrightarrow & 45x+12x& = & 8+20 \\\Leftrightarrow & \color{red}{57} x& = & 28 \\\Leftrightarrow & x = \frac{28}{57} & & \\ & V = \left\{ \frac{28}{57} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{6}{7} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1176x \color{red}{-147} & = & \color{red}{448x} +48 \\\Leftrightarrow & -1176x \color{red}{-147} \color{blue}{+147} \color{blue}{-448x} & = & \color{red}{448x} +48 \color{blue}{-448x} \color{blue}{+147} \\\Leftrightarrow & -1176x-448x& = & 48+147 \\\Leftrightarrow & \color{red}{-1624} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-1624} & & \\\Leftrightarrow & x = \frac{-195}{1624} & & \\ & V = \left\{ \frac{-195}{1624} \right\} & \\\end{align}\)