Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 9x-\frac{9}{5}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-99} & = & \color{red}{-110x} +40 \\\Leftrightarrow & 495x \color{red}{-99} \color{blue}{+99} \color{blue}{+110x} & = & \color{red}{-110x} +40 \color{blue}{+110x} \color{blue}{+99} \\\Leftrightarrow & 495x+110x& = & 40+99 \\\Leftrightarrow & \color{red}{605} x& = & 139 \\\Leftrightarrow & x = \frac{139}{605} & & \\ & V = \left\{ \frac{139}{605} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-44} & = & \color{red}{-495x} +30 \\\Leftrightarrow & 550x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +30 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & 550x+495x& = & 30+44 \\\Leftrightarrow & \color{red}{1045} x& = & 74 \\\Leftrightarrow & x = \frac{74}{1045} & & \\ & V = \left\{ \frac{74}{1045} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{5})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -35x+\frac{28}{5}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x+ \frac{308}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{+308} & = & \color{red}{-495x} +20 \\\Leftrightarrow & -1925x \color{red}{+308} \color{blue}{-308} \color{blue}{+495x} & = & \color{red}{-495x} +20 \color{blue}{+495x} \color{blue}{-308} \\\Leftrightarrow & -1925x+495x& = & 20-308 \\\Leftrightarrow & \color{red}{-1430} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{-1430} & & \\\Leftrightarrow & x = \frac{144}{715} & & \\ & V = \left\{ \frac{144}{715} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-168} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -420x \color{red}{-168} \color{blue}{+168} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+168} \\\Leftrightarrow & -420x+175x& = & 15+168 \\\Leftrightarrow & \color{red}{-245} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-245} & & \\\Leftrightarrow & x = \frac{-183}{245} & & \\ & V = \left\{ \frac{-183}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-200}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -200x \color{red}{+75} & = & \color{red}{-140x} +12 \\\Leftrightarrow & -200x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +12 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & -200x+140x& = & 12-75 \\\Leftrightarrow & \color{red}{-60} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-60} & & \\\Leftrightarrow & x = \frac{21}{20} & & \\ & V = \left\{ \frac{21}{20} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{11})& = & -6x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{20}{11}& = & -6x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{40}{ \color{blue}{22} })& = & (\frac{-132}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+40} & = & \color{red}{-132x} +33 \\\Leftrightarrow & 550x \color{red}{+40} \color{blue}{-40} \color{blue}{+132x} & = & \color{red}{-132x} +33 \color{blue}{+132x} \color{blue}{-40} \\\Leftrightarrow & 550x+132x& = & 33-40 \\\Leftrightarrow & \color{red}{682} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{682} & & \\ & V = \left\{ \frac{-7}{682} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{50x} +15 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-36} \\\Leftrightarrow & 180x-50x& = & 15-36 \\\Leftrightarrow & \color{red}{130} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{130} & & \\ & V = \left\{ \frac{-21}{130} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+60} & = & \color{red}{-45x} +8 \\\Leftrightarrow & 108x \color{red}{+60} \color{blue}{-60} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{-60} \\\Leftrightarrow & 108x+45x& = & 8-60 \\\Leftrightarrow & \color{red}{153} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{153} & & \\ & V = \left\{ \frac{-52}{153} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{7})& = & 8x+\frac{4}{5} \\\Leftrightarrow & -15x+\frac{9}{7}& = & 8x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+45} & = & \color{red}{280x} +28 \\\Leftrightarrow & -525x \color{red}{+45} \color{blue}{-45} \color{blue}{-280x} & = & \color{red}{280x} +28 \color{blue}{-280x} \color{blue}{-45} \\\Leftrightarrow & -525x-280x& = & 28-45 \\\Leftrightarrow & \color{red}{-805} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-805} & & \\\Leftrightarrow & x = \frac{17}{805} & & \\ & V = \left\{ \frac{17}{805} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-6} & = & \color{red}{35x} +4 \\\Leftrightarrow & -28x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -28x-35x& = & 4+6 \\\Leftrightarrow & \color{red}{-63} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-63} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{8}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+32} & = & \color{red}{-84x} +21 \\\Leftrightarrow & 560x \color{red}{+32} \color{blue}{-32} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{-32} \\\Leftrightarrow & 560x+84x& = & 21-32 \\\Leftrightarrow & \color{red}{644} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{644} & & \\ & V = \left\{ \frac{-11}{644} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -9x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-84} & = & \color{red}{-693x} +66 \\\Leftrightarrow & 1540x \color{red}{-84} \color{blue}{+84} \color{blue}{+693x} & = & \color{red}{-693x} +66 \color{blue}{+693x} \color{blue}{+84} \\\Leftrightarrow & 1540x+693x& = & 66+84 \\\Leftrightarrow & \color{red}{2233} x& = & 150 \\\Leftrightarrow & x = \frac{150}{2233} & & \\ & V = \left\{ \frac{150}{2233} \right\} & \\\end{align}\)