Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{96}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-96} & = & \color{red}{-280x} +21 \\\Leftrightarrow & 672x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 672x+280x& = & 21+96 \\\Leftrightarrow & \color{red}{952} x& = & 117 \\\Leftrightarrow & x = \frac{117}{952} & & \\ & V = \left\{ \frac{117}{952} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 420x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{245} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{245} & & \\ & V = \left\{ \frac{-74}{245} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{11})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -14x-\frac{28}{11}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1078}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1078x \color{red}{-196} & = & \color{red}{231x} +33 \\\Leftrightarrow & -1078x \color{red}{-196} \color{blue}{+196} \color{blue}{-231x} & = & \color{red}{231x} +33 \color{blue}{-231x} \color{blue}{+196} \\\Leftrightarrow & -1078x-231x& = & 33+196 \\\Leftrightarrow & \color{red}{-1309} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1309} & & \\\Leftrightarrow & x = \frac{-229}{1309} & & \\ & V = \left\{ \frac{-229}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & 3x+\frac{5}{4} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{45}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{-32} & = & \color{red}{108x} +45 \\\Leftrightarrow & -288x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +45 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & -288x-108x& = & 45+32 \\\Leftrightarrow & \color{red}{-396} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-396} & & \\\Leftrightarrow & x = \frac{-7}{36} & & \\ & V = \left\{ \frac{-7}{36} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +2 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 2+12 \\\Leftrightarrow & \color{red}{-85} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-85} & & \\\Leftrightarrow & x = \frac{-14}{85} & & \\ & V = \left\{ \frac{-14}{85} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1584}{ \color{blue}{132} }x- \frac{144}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1584x \color{red}{-144} & = & \color{red}{-660x} +77 \\\Leftrightarrow & 1584x \color{red}{-144} \color{blue}{+144} \color{blue}{+660x} & = & \color{red}{-660x} +77 \color{blue}{+660x} \color{blue}{+144} \\\Leftrightarrow & 1584x+660x& = & 77+144 \\\Leftrightarrow & \color{red}{2244} x& = & 221 \\\Leftrightarrow & x = \frac{221}{2244} & & \\\Leftrightarrow & x = \frac{13}{132} & & \\ & V = \left\{ \frac{13}{132} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{8})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{15}{8}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+45} & = & \color{red}{-168x} +16 \\\Leftrightarrow & 240x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +16 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & 240x+168x& = & 16-45 \\\Leftrightarrow & \color{red}{408} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{408} & & \\ & V = \left\{ \frac{-29}{408} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{+15} & = & \color{red}{-20x} +9 \\\Leftrightarrow & 24x \color{red}{+15} \color{blue}{-15} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{-15} \\\Leftrightarrow & 24x+20x& = & 9-15 \\\Leftrightarrow & \color{red}{44} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{44} & & \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{9})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{16}{9}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+16} & = & \color{red}{-81x} +30 \\\Leftrightarrow & -72x \color{red}{+16} \color{blue}{-16} \color{blue}{+81x} & = & \color{red}{-81x} +30 \color{blue}{+81x} \color{blue}{-16} \\\Leftrightarrow & -72x+81x& = & 30-16 \\\Leftrightarrow & \color{red}{9} x& = & 14 \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x-\frac{24}{11}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1584}{ \color{blue}{132} }x- \frac{288}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1584x \color{red}{-288} & = & \color{red}{660x} +77 \\\Leftrightarrow & 1584x \color{red}{-288} \color{blue}{+288} \color{blue}{-660x} & = & \color{red}{660x} +77 \color{blue}{-660x} \color{blue}{+288} \\\Leftrightarrow & 1584x-660x& = & 77+288 \\\Leftrightarrow & \color{red}{924} x& = & 365 \\\Leftrightarrow & x = \frac{365}{924} & & \\ & V = \left\{ \frac{365}{924} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{-108} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -360x \color{red}{-108} \color{blue}{+108} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+108} \\\Leftrightarrow & -360x+135x& = & 10+108 \\\Leftrightarrow & \color{red}{-225} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-225} & & \\\Leftrightarrow & x = \frac{-118}{225} & & \\ & V = \left\{ \frac{-118}{225} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +4 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 4-12 \\\Leftrightarrow & \color{red}{-85} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-85} & & \\\Leftrightarrow & x = \frac{8}{85} & & \\ & V = \left\{ \frac{8}{85} \right\} & \\\end{align}\)