Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{8}{3}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-48}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -48x \color{red}{-32} & = & \color{red}{108x} +9 \\\Leftrightarrow & -48x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +9 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & -48x-108x& = & 9+32 \\\Leftrightarrow & \color{red}{-156} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-156} & & \\\Leftrightarrow & x = \frac{-41}{156} & & \\ & V = \left\{ \frac{-41}{156} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{3})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -4x-\frac{10}{3}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-30} & = & \color{red}{81x} +10 \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-81x} & = & \color{red}{81x} +10 \color{blue}{-81x} \color{blue}{+30} \\\Leftrightarrow & -36x-81x& = & 10+30 \\\Leftrightarrow & \color{red}{-117} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-117} & & \\\Leftrightarrow & x = \frac{-40}{117} & & \\ & V = \left\{ \frac{-40}{117} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{7})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 25x+\frac{15}{7}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{+15} & = & \color{red}{-14x} +6 \\\Leftrightarrow & 175x \color{red}{+15} \color{blue}{-15} \color{blue}{+14x} & = & \color{red}{-14x} +6 \color{blue}{+14x} \color{blue}{-15} \\\Leftrightarrow & 175x+14x& = & 6-15 \\\Leftrightarrow & \color{red}{189} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{189} & & \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{10})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 9x-\frac{9}{10}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{990}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{20}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 990x \color{red}{-99} & = & \color{red}{550x} +20 \\\Leftrightarrow & 990x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +20 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & 990x-550x& = & 20+99 \\\Leftrightarrow & \color{red}{440} x& = & 119 \\\Leftrightarrow & x = \frac{119}{440} & & \\ & V = \left\{ \frac{119}{440} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+48} \\\Leftrightarrow & -660x+231x& = & 110+48 \\\Leftrightarrow & \color{red}{-429} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-429} & & \\\Leftrightarrow & x = \frac{-158}{429} & & \\ & V = \left\{ \frac{-158}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-66} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 770x \color{red}{-66} \color{blue}{+66} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{+66} \\\Leftrightarrow & 770x+693x& = & 42+66 \\\Leftrightarrow & \color{red}{1463} x& = & 108 \\\Leftrightarrow & x = \frac{108}{1463} & & \\ & V = \left\{ \frac{108}{1463} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{105x} +20 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 450x-105x& = & 20-72 \\\Leftrightarrow & \color{red}{345} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{345} & & \\ & V = \left\{ \frac{-52}{345} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{330x} +99 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-330x} & = & \color{red}{330x} +99 \color{blue}{-330x} \color{blue}{+180} \\\Leftrightarrow & -1980x-330x& = & 99+180 \\\Leftrightarrow & \color{red}{-2310} x& = & 279 \\\Leftrightarrow & x = \frac{279}{-2310} & & \\\Leftrightarrow & x = \frac{-93}{770} & & \\ & V = \left\{ \frac{-93}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{10}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{+100} & = & \color{red}{550x} +99 \\\Leftrightarrow & 660x \color{red}{+100} \color{blue}{-100} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-100} \\\Leftrightarrow & 660x-550x& = & 99-100 \\\Leftrightarrow & \color{red}{110} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{110} & & \\ & V = \left\{ \frac{-1}{110} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 8x+\frac{8}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+40} & = & \color{red}{275x} +88 \\\Leftrightarrow & 440x \color{red}{+40} \color{blue}{-40} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{-40} \\\Leftrightarrow & 440x-275x& = & 88-40 \\\Leftrightarrow & \color{red}{165} x& = & 48 \\\Leftrightarrow & x = \frac{48}{165} & & \\\Leftrightarrow & x = \frac{16}{55} & & \\ & V = \left\{ \frac{16}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{+32} & = & \color{red}{60x} +9 \\\Leftrightarrow & -144x \color{red}{+32} \color{blue}{-32} \color{blue}{-60x} & = & \color{red}{60x} +9 \color{blue}{-60x} \color{blue}{-32} \\\Leftrightarrow & -144x-60x& = & 9-32 \\\Leftrightarrow & \color{red}{-204} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-204} & & \\\Leftrightarrow & x = \frac{23}{204} & & \\ & V = \left\{ \frac{23}{204} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{2})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-125} & = & \color{red}{90x} +8 \\\Leftrightarrow & -200x \color{red}{-125} \color{blue}{+125} \color{blue}{-90x} & = & \color{red}{90x} +8 \color{blue}{-90x} \color{blue}{+125} \\\Leftrightarrow & -200x-90x& = & 8+125 \\\Leftrightarrow & \color{red}{-290} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-290} & & \\\Leftrightarrow & x = \frac{-133}{290} & & \\ & V = \left\{ \frac{-133}{290} \right\} & \\\end{align}\)