Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 10x-\frac{15}{11}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-15} & = & \color{red}{-77x} +9 \\\Leftrightarrow & 110x \color{red}{-15} \color{blue}{+15} \color{blue}{+77x} & = & \color{red}{-77x} +9 \color{blue}{+77x} \color{blue}{+15} \\\Leftrightarrow & 110x+77x& = & 9+15 \\\Leftrightarrow & \color{red}{187} x& = & 24 \\\Leftrightarrow & x = \frac{24}{187} & & \\ & V = \left\{ \frac{24}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{6})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{-270x} +24 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{+270x} & = & \color{red}{-270x} +24 \color{blue}{+270x} \color{blue}{-175} \\\Leftrightarrow & 420x+270x& = & 24-175 \\\Leftrightarrow & \color{red}{690} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{690} & & \\ & V = \left\{ \frac{-151}{690} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+30} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 660x \color{red}{+30} \color{blue}{-30} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-30} \\\Leftrightarrow & 660x+231x& = & 44-30 \\\Leftrightarrow & \color{red}{891} x& = & 14 \\\Leftrightarrow & x = \frac{14}{891} & & \\ & V = \left\{ \frac{14}{891} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{7})& = & -8x+\frac{9}{8} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-48} & = & \color{red}{-448x} +63 \\\Leftrightarrow & -840x \color{red}{-48} \color{blue}{+48} \color{blue}{+448x} & = & \color{red}{-448x} +63 \color{blue}{+448x} \color{blue}{+48} \\\Leftrightarrow & -840x+448x& = & 63+48 \\\Leftrightarrow & \color{red}{-392} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-392} & & \\\Leftrightarrow & x = \frac{-111}{392} & & \\ & V = \left\{ \frac{-111}{392} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{105x} +28 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 140x-105x& = & 28+30 \\\Leftrightarrow & \color{red}{35} x& = & 58 \\\Leftrightarrow & x = \frac{58}{35} & & \\ & V = \left\{ \frac{58}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{2})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 14x+\frac{21}{2}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{105}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+105} & = & \color{red}{-30x} +16 \\\Leftrightarrow & 140x \color{red}{+105} \color{blue}{-105} \color{blue}{+30x} & = & \color{red}{-30x} +16 \color{blue}{+30x} \color{blue}{-105} \\\Leftrightarrow & 140x+30x& = & 16-105 \\\Leftrightarrow & \color{red}{170} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{170} & & \\ & V = \left\{ \frac{-89}{170} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{10}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+70} & = & \color{red}{-147x} +30 \\\Leftrightarrow & 84x \color{red}{+70} \color{blue}{-70} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{-70} \\\Leftrightarrow & 84x+147x& = & 30-70 \\\Leftrightarrow & \color{red}{231} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{231} & & \\ & V = \left\{ \frac{-40}{231} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{+48} & = & \color{red}{280x} +49 \\\Leftrightarrow & 672x \color{red}{+48} \color{blue}{-48} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{-48} \\\Leftrightarrow & 672x-280x& = & 49-48 \\\Leftrightarrow & \color{red}{392} x& = & 1 \\\Leftrightarrow & x = \frac{1}{392} & & \\ & V = \left\{ \frac{1}{392} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+48} & = & \color{red}{-45x} +7 \\\Leftrightarrow & -108x \color{red}{+48} \color{blue}{-48} \color{blue}{+45x} & = & \color{red}{-45x} +7 \color{blue}{+45x} \color{blue}{-48} \\\Leftrightarrow & -108x+45x& = & 7-48 \\\Leftrightarrow & \color{red}{-63} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-63} & & \\\Leftrightarrow & x = \frac{41}{63} & & \\ & V = \left\{ \frac{41}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{539x} +14 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & 770x-539x& = & 14-110 \\\Leftrightarrow & \color{red}{231} x& = & -96 \\\Leftrightarrow & x = \frac{-96}{231} & & \\\Leftrightarrow & x = \frac{-32}{77} & & \\ & V = \left\{ \frac{-32}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+140} & = & \color{red}{147x} +18 \\\Leftrightarrow & 168x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & 168x-147x& = & 18-140 \\\Leftrightarrow & \color{red}{21} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{21} & & \\ & V = \left\{ \frac{-122}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+42} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -462x \color{red}{+42} \color{blue}{-42} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-42} \\\Leftrightarrow & -462x+539x& = & 110-42 \\\Leftrightarrow & \color{red}{77} x& = & 68 \\\Leftrightarrow & x = \frac{68}{77} & & \\ & V = \left\{ \frac{68}{77} \right\} & \\\end{align}\)