Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{6}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x- \frac{48}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{-280x} +35 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+48} \\\Leftrightarrow & -240x+280x& = & 35+48 \\\Leftrightarrow & \color{red}{40} x& = & 83 \\\Leftrightarrow & x = \frac{83}{40} & & \\ & V = \left\{ \frac{83}{40} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 28x-\frac{28}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{-196} & = & \color{red}{385x} +22 \\\Leftrightarrow & 2156x \color{red}{-196} \color{blue}{+196} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+196} \\\Leftrightarrow & 2156x-385x& = & 22+196 \\\Leftrightarrow & \color{red}{1771} x& = & 218 \\\Leftrightarrow & x = \frac{218}{1771} & & \\ & V = \left\{ \frac{218}{1771} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{11})& = & -8x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{21}{11}& = & -8x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1540}{ \color{blue}{44} }x+ \frac{84}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1540x \color{red}{+84} & = & \color{red}{-352x} +33 \\\Leftrightarrow & 1540x \color{red}{+84} \color{blue}{-84} \color{blue}{+352x} & = & \color{red}{-352x} +33 \color{blue}{+352x} \color{blue}{-84} \\\Leftrightarrow & 1540x+352x& = & 33-84 \\\Leftrightarrow & \color{red}{1892} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{1892} & & \\ & V = \left\{ \frac{-51}{1892} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+12} & = & \color{red}{70x} +21 \\\Leftrightarrow & 168x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & 168x-70x& = & 21-12 \\\Leftrightarrow & \color{red}{98} x& = & 9 \\\Leftrightarrow & x = \frac{9}{98} & & \\ & V = \left\{ \frac{9}{98} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{-24} & = & \color{red}{-63x} +7 \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & 36x+63x& = & 7+24 \\\Leftrightarrow & \color{red}{99} x& = & 31 \\\Leftrightarrow & x = \frac{31}{99} & & \\ & V = \left\{ \frac{31}{99} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 10x+\frac{25}{6}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{660}{ \color{blue}{66} }x+ \frac{275}{ \color{blue}{66} })& = & (\frac{-594}{ \color{blue}{66} }x+ \frac{48}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 660x \color{red}{+275} & = & \color{red}{-594x} +48 \\\Leftrightarrow & 660x \color{red}{+275} \color{blue}{-275} \color{blue}{+594x} & = & \color{red}{-594x} +48 \color{blue}{+594x} \color{blue}{-275} \\\Leftrightarrow & 660x+594x& = & 48-275 \\\Leftrightarrow & \color{red}{1254} x& = & -227 \\\Leftrightarrow & x = \frac{-227}{1254} & & \\ & V = \left\{ \frac{-227}{1254} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{15}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-135} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -990x \color{red}{-135} \color{blue}{+135} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{+135} \\\Leftrightarrow & -990x+693x& = & 22+135 \\\Leftrightarrow & \color{red}{-297} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-297} & & \\\Leftrightarrow & x = \frac{-157}{297} & & \\ & V = \left\{ \frac{-157}{297} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 9x+\frac{3}{11} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+330} & = & \color{red}{693x} +21 \\\Leftrightarrow & -1386x \color{red}{+330} \color{blue}{-330} \color{blue}{-693x} & = & \color{red}{693x} +21 \color{blue}{-693x} \color{blue}{-330} \\\Leftrightarrow & -1386x-693x& = & 21-330 \\\Leftrightarrow & \color{red}{-2079} x& = & -309 \\\Leftrightarrow & x = \frac{-309}{-2079} & & \\\Leftrightarrow & x = \frac{103}{693} & & \\ & V = \left\{ \frac{103}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{18}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-90} \\\Leftrightarrow & -990x+495x& = & 22-90 \\\Leftrightarrow & \color{red}{-495} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-495} & & \\\Leftrightarrow & x = \frac{68}{495} & & \\ & V = \left\{ \frac{68}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{12}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{-550x} +99 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{-120} \\\Leftrightarrow & -1320x+550x& = & 99-120 \\\Leftrightarrow & \color{red}{-770} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-770} & & \\\Leftrightarrow & x = \frac{3}{110} & & \\ & V = \left\{ \frac{3}{110} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{8}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-8} & = & \color{red}{63x} +10 \\\Leftrightarrow & 70x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & 70x-63x& = & 10+8 \\\Leftrightarrow & \color{red}{7} x& = & 18 \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-84} & = & \color{red}{245x} +40 \\\Leftrightarrow & -700x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & -700x-245x& = & 40+84 \\\Leftrightarrow & \color{red}{-945} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-945} & & \\\Leftrightarrow & x = \frac{-124}{945} & & \\ & V = \left\{ \frac{-124}{945} \right\} & \\\end{align}\)