Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{50x} +15 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 60x-50x& = & 15-12 \\\Leftrightarrow & \color{red}{10} x& = & 3 \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{7}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+220} & = & \color{red}{693x} +35 \\\Leftrightarrow & -616x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +35 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & -616x-693x& = & 35-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-1309} & & \\\Leftrightarrow & x = \frac{185}{1309} & & \\ & V = \left\{ \frac{185}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{5})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{-132} & = & \color{red}{-495x} +40 \\\Leftrightarrow & 1100x \color{red}{-132} \color{blue}{+132} \color{blue}{+495x} & = & \color{red}{-495x} +40 \color{blue}{+495x} \color{blue}{+132} \\\Leftrightarrow & 1100x+495x& = & 40+132 \\\Leftrightarrow & \color{red}{1595} x& = & 172 \\\Leftrightarrow & x = \frac{172}{1595} & & \\ & V = \left\{ \frac{172}{1595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-231} & = & \color{red}{-264x} +48 \\\Leftrightarrow & 2464x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +48 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & 2464x+264x& = & 48+231 \\\Leftrightarrow & \color{red}{2728} x& = & 279 \\\Leftrightarrow & x = \frac{279}{2728} & & \\\Leftrightarrow & x = \frac{9}{88} & & \\ & V = \left\{ \frac{9}{88} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x+ \frac{200}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{+200} & = & \color{red}{490x} +63 \\\Leftrightarrow & 840x \color{red}{+200} \color{blue}{-200} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-200} \\\Leftrightarrow & 840x-490x& = & 63-200 \\\Leftrightarrow & \color{red}{350} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{350} & & \\ & V = \left\{ \frac{-137}{350} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+90} & = & \color{red}{275x} +66 \\\Leftrightarrow & 1320x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & 1320x-275x& = & 66-90 \\\Leftrightarrow & \color{red}{1045} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{1045} & & \\ & V = \left\{ \frac{-24}{1045} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{2})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{25}{2}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-125} & = & \color{red}{70x} +12 \\\Leftrightarrow & -100x \color{red}{-125} \color{blue}{+125} \color{blue}{-70x} & = & \color{red}{70x} +12 \color{blue}{-70x} \color{blue}{+125} \\\Leftrightarrow & -100x-70x& = & 12+125 \\\Leftrightarrow & \color{red}{-170} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-170} & & \\\Leftrightarrow & x = \frac{-137}{170} & & \\ & V = \left\{ \frac{-137}{170} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{12}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{704}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 704x \color{red}{-96} & = & \color{red}{440x} +77 \\\Leftrightarrow & 704x \color{red}{-96} \color{blue}{+96} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{+96} \\\Leftrightarrow & 704x-440x& = & 77+96 \\\Leftrightarrow & \color{red}{264} x& = & 173 \\\Leftrightarrow & x = \frac{173}{264} & & \\ & V = \left\{ \frac{173}{264} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-48} & = & \color{red}{-189x} +70 \\\Leftrightarrow & -168x \color{red}{-48} \color{blue}{+48} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+48} \\\Leftrightarrow & -168x+189x& = & 70+48 \\\Leftrightarrow & \color{red}{21} x& = & 118 \\\Leftrightarrow & x = \frac{118}{21} & & \\ & V = \left\{ \frac{118}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{12})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{35}{12}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-35} & = & \color{red}{108x} +54 \\\Leftrightarrow & -420x \color{red}{-35} \color{blue}{+35} \color{blue}{-108x} & = & \color{red}{108x} +54 \color{blue}{-108x} \color{blue}{+35} \\\Leftrightarrow & -420x-108x& = & 54+35 \\\Leftrightarrow & \color{red}{-528} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-528} & & \\\Leftrightarrow & x = \frac{-89}{528} & & \\ & V = \left\{ \frac{-89}{528} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -4x+\frac{10}{9}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-144}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -144x \color{red}{+40} & = & \color{red}{-180x} +81 \\\Leftrightarrow & -144x \color{red}{+40} \color{blue}{-40} \color{blue}{+180x} & = & \color{red}{-180x} +81 \color{blue}{+180x} \color{blue}{-40} \\\Leftrightarrow & -144x+180x& = & 81-40 \\\Leftrightarrow & \color{red}{36} x& = & 41 \\\Leftrightarrow & x = \frac{41}{36} & & \\ & V = \left\{ \frac{41}{36} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{9})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -28x-\frac{14}{9}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-154} & = & \color{red}{-495x} +72 \\\Leftrightarrow & -2772x \color{red}{-154} \color{blue}{+154} \color{blue}{+495x} & = & \color{red}{-495x} +72 \color{blue}{+495x} \color{blue}{+154} \\\Leftrightarrow & -2772x+495x& = & 72+154 \\\Leftrightarrow & \color{red}{-2277} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-2277} & & \\\Leftrightarrow & x = \frac{-226}{2277} & & \\ & V = \left\{ \frac{-226}{2277} \right\} & \\\end{align}\)