Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{1}{2})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{5}{2}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x- \frac{10}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{-10} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -100x \color{red}{-10} \color{blue}{+10} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{+10} \\\Leftrightarrow & -100x+20x& = & 9+10 \\\Leftrightarrow & \color{red}{-80} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-80} & & \\\Leftrightarrow & x = \frac{-19}{80} & & \\ & V = \left\{ \frac{-19}{80} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{9})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{20}{9}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{-20} & = & \color{red}{-63x} +10 \\\Leftrightarrow & 135x \color{red}{-20} \color{blue}{+20} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+20} \\\Leftrightarrow & 135x+63x& = & 10+20 \\\Leftrightarrow & \color{red}{198} x& = & 30 \\\Leftrightarrow & x = \frac{30}{198} & & \\\Leftrightarrow & x = \frac{5}{33} & & \\ & V = \left\{ \frac{5}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -24x+\frac{30}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{+60} & = & \color{red}{154x} +77 \\\Leftrightarrow & -528x \color{red}{+60} \color{blue}{-60} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{-60} \\\Leftrightarrow & -528x-154x& = & 77-60 \\\Leftrightarrow & \color{red}{-682} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-682} & & \\\Leftrightarrow & x = \frac{-17}{682} & & \\ & V = \left\{ \frac{-17}{682} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-216} & = & \color{red}{-225x} +10 \\\Leftrightarrow & 810x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 810x+225x& = & 10+216 \\\Leftrightarrow & \color{red}{1035} x& = & 226 \\\Leftrightarrow & x = \frac{226}{1035} & & \\ & V = \left\{ \frac{226}{1035} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 6x+\frac{5}{6} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 6x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{+63} & = & \color{red}{144x} +20 \\\Leftrightarrow & -840x \color{red}{+63} \color{blue}{-63} \color{blue}{-144x} & = & \color{red}{144x} +20 \color{blue}{-144x} \color{blue}{-63} \\\Leftrightarrow & -840x-144x& = & 20-63 \\\Leftrightarrow & \color{red}{-984} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-984} & & \\\Leftrightarrow & x = \frac{43}{984} & & \\ & V = \left\{ \frac{43}{984} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{25}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{275}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-275} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 770x \color{red}{-275} \color{blue}{+275} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{+275} \\\Leftrightarrow & 770x+231x& = & 42+275 \\\Leftrightarrow & \color{red}{1001} x& = & 317 \\\Leftrightarrow & x = \frac{317}{1001} & & \\ & V = \left\{ \frac{317}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-49x} +2 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+49x} & = & \color{red}{-49x} +2 \color{blue}{+49x} \color{blue}{+30} \\\Leftrightarrow & -210x+49x& = & 2+30 \\\Leftrightarrow & \color{red}{-161} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-161} & & \\\Leftrightarrow & x = \frac{-32}{161} & & \\ & V = \left\{ \frac{-32}{161} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{-60x} +32 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{+60x} & = & \color{red}{-60x} +32 \color{blue}{+60x} \color{blue}{+45} \\\Leftrightarrow & 72x+60x& = & 32+45 \\\Leftrightarrow & \color{red}{132} x& = & 77 \\\Leftrightarrow & x = \frac{77}{132} & & \\\Leftrightarrow & x = \frac{7}{12} & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+24} & = & \color{red}{55x} +5 \\\Leftrightarrow & -264x \color{red}{+24} \color{blue}{-24} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-24} \\\Leftrightarrow & -264x-55x& = & 5-24 \\\Leftrightarrow & \color{red}{-319} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-319} & & \\\Leftrightarrow & x = \frac{19}{319} & & \\ & V = \left\{ \frac{19}{319} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -9x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+64} & = & \color{red}{-252x} +21 \\\Leftrightarrow & 560x \color{red}{+64} \color{blue}{-64} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-64} \\\Leftrightarrow & 560x+252x& = & 21-64 \\\Leftrightarrow & \color{red}{812} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{812} & & \\ & V = \left\{ \frac{-43}{812} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{+8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 144x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 144x+63x& = & 6-8 \\\Leftrightarrow & \color{red}{207} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{207} & & \\ & V = \left\{ \frac{-2}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{12})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 20x-\frac{25}{12}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2640}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{24}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2640x \color{red}{-275} & = & \color{red}{-924x} +24 \\\Leftrightarrow & 2640x \color{red}{-275} \color{blue}{+275} \color{blue}{+924x} & = & \color{red}{-924x} +24 \color{blue}{+924x} \color{blue}{+275} \\\Leftrightarrow & 2640x+924x& = & 24+275 \\\Leftrightarrow & \color{red}{3564} x& = & 299 \\\Leftrightarrow & x = \frac{299}{3564} & & \\ & V = \left\{ \frac{299}{3564} \right\} & \\\end{align}\)