Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-72} \\\Leftrightarrow & -450x+105x& = & 20-72 \\\Leftrightarrow & \color{red}{-345} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-345} & & \\\Leftrightarrow & x = \frac{52}{345} & & \\ & V = \left\{ \frac{52}{345} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+88} & = & \color{red}{-297x} +24 \\\Leftrightarrow & -132x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +24 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & -132x+297x& = & 24-88 \\\Leftrightarrow & \color{red}{165} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{165} & & \\ & V = \left\{ \frac{-64}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{7})& = & -8x+\frac{3}{10} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{-60} & = & \color{red}{-560x} +21 \\\Leftrightarrow & -1050x \color{red}{-60} \color{blue}{+60} \color{blue}{+560x} & = & \color{red}{-560x} +21 \color{blue}{+560x} \color{blue}{+60} \\\Leftrightarrow & -1050x+560x& = & 21+60 \\\Leftrightarrow & \color{red}{-490} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-490} & & \\\Leftrightarrow & x = \frac{-81}{490} & & \\ & V = \left\{ \frac{-81}{490} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{7})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 16x-\frac{8}{7}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{-8} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 112x \color{red}{-8} \color{blue}{+8} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+8} \\\Leftrightarrow & 112x+35x& = & 4+8 \\\Leftrightarrow & \color{red}{147} x& = & 12 \\\Leftrightarrow & x = \frac{12}{147} & & \\\Leftrightarrow & x = \frac{4}{49} & & \\ & V = \left\{ \frac{4}{49} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{12}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+60} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -660x \color{red}{+60} \color{blue}{-60} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-60} \\\Leftrightarrow & -660x+275x& = & 66-60 \\\Leftrightarrow & \color{red}{-385} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-385} & & \\\Leftrightarrow & x = \frac{-6}{385} & & \\ & V = \left\{ \frac{-6}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-21} & = & \color{red}{-72x} +36 \\\Leftrightarrow & 112x \color{red}{-21} \color{blue}{+21} \color{blue}{+72x} & = & \color{red}{-72x} +36 \color{blue}{+72x} \color{blue}{+21} \\\Leftrightarrow & 112x+72x& = & 36+21 \\\Leftrightarrow & \color{red}{184} x& = & 57 \\\Leftrightarrow & x = \frac{57}{184} & & \\ & V = \left\{ \frac{57}{184} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -84x+35x& = & 6+30 \\\Leftrightarrow & \color{red}{-49} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-49} & & \\\Leftrightarrow & x = \frac{-36}{49} & & \\ & V = \left\{ \frac{-36}{49} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{+40} & = & \color{red}{84x} +15 \\\Leftrightarrow & -72x \color{red}{+40} \color{blue}{-40} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{-40} \\\Leftrightarrow & -72x-84x& = & 15-40 \\\Leftrightarrow & \color{red}{-156} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-156} & & \\\Leftrightarrow & x = \frac{25}{156} & & \\ & V = \left\{ \frac{25}{156} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{7})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 30x+\frac{24}{7}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{2100}{ \color{blue}{70} }x+ \frac{240}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 2100x \color{red}{+240} & = & \color{red}{490x} +49 \\\Leftrightarrow & 2100x \color{red}{+240} \color{blue}{-240} \color{blue}{-490x} & = & \color{red}{490x} +49 \color{blue}{-490x} \color{blue}{-240} \\\Leftrightarrow & 2100x-490x& = & 49-240 \\\Leftrightarrow & \color{red}{1610} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{1610} & & \\ & V = \left\{ \frac{-191}{1610} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{45x} +40 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{+18} \\\Leftrightarrow & 60x-45x& = & 40+18 \\\Leftrightarrow & \color{red}{15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{15} & & \\ & V = \left\{ \frac{58}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{+36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -528x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & -528x+110x& = & 33-36 \\\Leftrightarrow & \color{red}{-418} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-418} & & \\\Leftrightarrow & x = \frac{3}{418} & & \\ & V = \left\{ \frac{3}{418} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{35x} +6 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -63x-35x& = & 6+6 \\\Leftrightarrow & \color{red}{-98} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-98} & & \\\Leftrightarrow & x = \frac{-6}{49} & & \\ & V = \left\{ \frac{-6}{49} \right\} & \\\end{align}\)