Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -24x-\frac{12}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{-36} & = & \color{red}{147x} +14 \\\Leftrightarrow & -504x \color{red}{-36} \color{blue}{+36} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+36} \\\Leftrightarrow & -504x-147x& = & 14+36 \\\Leftrightarrow & \color{red}{-651} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-651} & & \\\Leftrightarrow & x = \frac{-50}{651} & & \\ & V = \left\{ \frac{-50}{651} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{7})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{4}{7}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{16}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-16} & = & \color{red}{-196x} +63 \\\Leftrightarrow & 280x \color{red}{-16} \color{blue}{+16} \color{blue}{+196x} & = & \color{red}{-196x} +63 \color{blue}{+196x} \color{blue}{+16} \\\Leftrightarrow & 280x+196x& = & 63+16 \\\Leftrightarrow & \color{red}{476} x& = & 79 \\\Leftrightarrow & x = \frac{79}{476} & & \\ & V = \left\{ \frac{79}{476} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{9})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{35}{9}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-245} & = & \color{red}{189x} +27 \\\Leftrightarrow & 882x \color{red}{-245} \color{blue}{+245} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{+245} \\\Leftrightarrow & 882x-189x& = & 27+245 \\\Leftrightarrow & \color{red}{693} x& = & 272 \\\Leftrightarrow & x = \frac{272}{693} & & \\ & V = \left\{ \frac{272}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{441x} +28 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & -378x-441x& = & 28-90 \\\Leftrightarrow & \color{red}{-819} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-819} & & \\\Leftrightarrow & x = \frac{62}{819} & & \\ & V = \left\{ \frac{62}{819} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-396}{ \color{blue}{66} }x- \frac{60}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -396x \color{red}{-60} & = & \color{red}{-462x} +77 \\\Leftrightarrow & -396x \color{red}{-60} \color{blue}{+60} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{+60} \\\Leftrightarrow & -396x+462x& = & 77+60 \\\Leftrightarrow & \color{red}{66} x& = & 137 \\\Leftrightarrow & x = \frac{137}{66} & & \\ & V = \left\{ \frac{137}{66} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+88} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -528x \color{red}{+88} \color{blue}{-88} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-88} \\\Leftrightarrow & -528x+231x& = & 18-88 \\\Leftrightarrow & \color{red}{-297} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-297} & & \\\Leftrightarrow & x = \frac{70}{297} & & \\ & V = \left\{ \frac{70}{297} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & 9x+\frac{5}{4} \\\Leftrightarrow & 14x-\frac{21}{8}& = & 9x+\frac{5}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{10}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-21} & = & \color{red}{72x} +10 \\\Leftrightarrow & 112x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & 112x-72x& = & 10+21 \\\Leftrightarrow & \color{red}{40} x& = & 31 \\\Leftrightarrow & x = \frac{31}{40} & & \\ & V = \left\{ \frac{31}{40} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{6}{11}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+12} & = & \color{red}{-88x} +77 \\\Leftrightarrow & 330x \color{red}{+12} \color{blue}{-12} \color{blue}{+88x} & = & \color{red}{-88x} +77 \color{blue}{+88x} \color{blue}{-12} \\\Leftrightarrow & 330x+88x& = & 77-12 \\\Leftrightarrow & \color{red}{418} x& = & 65 \\\Leftrightarrow & x = \frac{65}{418} & & \\ & V = \left\{ \frac{65}{418} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{7})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 35x+4& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{36}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+36} & = & \color{red}{18x} +10 \\\Leftrightarrow & 315x \color{red}{+36} \color{blue}{-36} \color{blue}{-18x} & = & \color{red}{18x} +10 \color{blue}{-18x} \color{blue}{-36} \\\Leftrightarrow & 315x-18x& = & 10-36 \\\Leftrightarrow & \color{red}{297} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{297} & & \\ & V = \left\{ \frac{-26}{297} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+108} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -270x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -270x+315x& = & 20-108 \\\Leftrightarrow & \color{red}{45} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{45} & & \\ & V = \left\{ \frac{-88}{45} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+96} & = & \color{red}{-360x} +15 \\\Leftrightarrow & -320x \color{red}{+96} \color{blue}{-96} \color{blue}{+360x} & = & \color{red}{-360x} +15 \color{blue}{+360x} \color{blue}{-96} \\\Leftrightarrow & -320x+360x& = & 15-96 \\\Leftrightarrow & \color{red}{40} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{40} & & \\ & V = \left\{ \frac{-81}{40} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 210x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{35} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{35} & & \\ & V = \left\{ \frac{-74}{35} \right\} & \\\end{align}\)