Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & 2x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-90} & = & \color{red}{110x} +66 \\\Leftrightarrow & -990x \color{red}{-90} \color{blue}{+90} \color{blue}{-110x} & = & \color{red}{110x} +66 \color{blue}{-110x} \color{blue}{+90} \\\Leftrightarrow & -990x-110x& = & 66+90 \\\Leftrightarrow & \color{red}{-1100} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-1100} & & \\\Leftrightarrow & x = \frac{-39}{275} & & \\ & V = \left\{ \frac{-39}{275} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{8})& = & 4x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{288}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+135} & = & \color{red}{288x} +32 \\\Leftrightarrow & -1080x \color{red}{+135} \color{blue}{-135} \color{blue}{-288x} & = & \color{red}{288x} +32 \color{blue}{-288x} \color{blue}{-135} \\\Leftrightarrow & -1080x-288x& = & 32-135 \\\Leftrightarrow & \color{red}{-1368} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-1368} & & \\\Leftrightarrow & x = \frac{103}{1368} & & \\ & V = \left\{ \frac{103}{1368} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 60x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{85} & & \\ & V = \left\{ \frac{-6}{85} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{8})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 6x-\frac{9}{8}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x- \frac{45}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{24}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{-45} & = & \color{red}{200x} +24 \\\Leftrightarrow & 240x \color{red}{-45} \color{blue}{+45} \color{blue}{-200x} & = & \color{red}{200x} +24 \color{blue}{-200x} \color{blue}{+45} \\\Leftrightarrow & 240x-200x& = & 24+45 \\\Leftrightarrow & \color{red}{40} x& = & 69 \\\Leftrightarrow & x = \frac{69}{40} & & \\ & V = \left\{ \frac{69}{40} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & 8x+\frac{8}{9} \\\Leftrightarrow & -15x+\frac{6}{11}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{+54} & = & \color{red}{792x} +88 \\\Leftrightarrow & -1485x \color{red}{+54} \color{blue}{-54} \color{blue}{-792x} & = & \color{red}{792x} +88 \color{blue}{-792x} \color{blue}{-54} \\\Leftrightarrow & -1485x-792x& = & 88-54 \\\Leftrightarrow & \color{red}{-2277} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-2277} & & \\\Leftrightarrow & x = \frac{-34}{2277} & & \\ & V = \left\{ \frac{-34}{2277} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-140} & = & \color{red}{63x} +6 \\\Leftrightarrow & 168x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & 168x-63x& = & 6+140 \\\Leftrightarrow & \color{red}{105} x& = & 146 \\\Leftrightarrow & x = \frac{146}{105} & & \\ & V = \left\{ \frac{146}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{11})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 6x+\frac{12}{11}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+84} & = & \color{red}{385x} +55 \\\Leftrightarrow & 462x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +55 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & 462x-385x& = & 55-84 \\\Leftrightarrow & \color{red}{77} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{77} & & \\ & V = \left\{ \frac{-29}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{10}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+50} & = & \color{red}{135x} +54 \\\Leftrightarrow & -360x \color{red}{+50} \color{blue}{-50} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-50} \\\Leftrightarrow & -360x-135x& = & 54-50 \\\Leftrightarrow & \color{red}{-495} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-495} & & \\\Leftrightarrow & x = \frac{-4}{495} & & \\ & V = \left\{ \frac{-4}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{+144} & = & \color{red}{616x} +33 \\\Leftrightarrow & 1584x \color{red}{+144} \color{blue}{-144} \color{blue}{-616x} & = & \color{red}{616x} +33 \color{blue}{-616x} \color{blue}{-144} \\\Leftrightarrow & 1584x-616x& = & 33-144 \\\Leftrightarrow & \color{red}{968} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{968} & & \\ & V = \left\{ \frac{-111}{968} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+220} & = & \color{red}{539x} +35 \\\Leftrightarrow & -1232x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -1232x-539x& = & 35-220 \\\Leftrightarrow & \color{red}{-1771} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-1771} & & \\\Leftrightarrow & x = \frac{185}{1771} & & \\ & V = \left\{ \frac{185}{1771} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{6})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{35}{6}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-35} & = & \color{red}{-18x} +20 \\\Leftrightarrow & -84x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +20 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & -84x+18x& = & 20+35 \\\Leftrightarrow & \color{red}{-66} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-66} & & \\\Leftrightarrow & x = \frac{-5}{6} & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{-200x} +25 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{+200x} & = & \color{red}{-200x} +25 \color{blue}{+200x} \color{blue}{+96} \\\Leftrightarrow & 480x+200x& = & 25+96 \\\Leftrightarrow & \color{red}{680} x& = & 121 \\\Leftrightarrow & x = \frac{121}{680} & & \\ & V = \left\{ \frac{121}{680} \right\} & \\\end{align}\)