Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -6x-\frac{6}{11}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-6} & = & \color{red}{77x} +9 \\\Leftrightarrow & -66x \color{red}{-6} \color{blue}{+6} \color{blue}{-77x} & = & \color{red}{77x} +9 \color{blue}{-77x} \color{blue}{+6} \\\Leftrightarrow & -66x-77x& = & 9+6 \\\Leftrightarrow & \color{red}{-143} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-143} & & \\\Leftrightarrow & x = \frac{-15}{143} & & \\ & V = \left\{ \frac{-15}{143} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-176} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 924x \color{red}{-176} \color{blue}{+176} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+176} \\\Leftrightarrow & 924x+385x& = & 42+176 \\\Leftrightarrow & \color{red}{1309} x& = & 218 \\\Leftrightarrow & x = \frac{218}{1309} & & \\ & V = \left\{ \frac{218}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{+99} & = & \color{red}{-550x} +50 \\\Leftrightarrow & 660x \color{red}{+99} \color{blue}{-99} \color{blue}{+550x} & = & \color{red}{-550x} +50 \color{blue}{+550x} \color{blue}{-99} \\\Leftrightarrow & 660x+550x& = & 50-99 \\\Leftrightarrow & \color{red}{1210} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{1210} & & \\ & V = \left\{ \frac{-49}{1210} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{-539x} +56 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+176} \\\Leftrightarrow & -1232x+539x& = & 56+176 \\\Leftrightarrow & \color{red}{-693} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-693} & & \\\Leftrightarrow & x = \frac{-232}{693} & & \\ & V = \left\{ \frac{-232}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{15}{8}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-15} & = & \color{red}{40x} +12 \\\Leftrightarrow & -96x \color{red}{-15} \color{blue}{+15} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{+15} \\\Leftrightarrow & -96x-40x& = & 12+15 \\\Leftrightarrow & \color{red}{-136} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-136} & & \\\Leftrightarrow & x = \frac{-27}{136} & & \\ & V = \left\{ \frac{-27}{136} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 4x+\frac{8}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+72} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 396x \color{red}{+72} \color{blue}{-72} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-72} \\\Leftrightarrow & 396x+495x& = & 22-72 \\\Leftrightarrow & \color{red}{891} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{891} & & \\ & V = \left\{ \frac{-50}{891} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{8}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{297x} +88 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{-24} \\\Leftrightarrow & -132x-297x& = & 88-24 \\\Leftrightarrow & \color{red}{-429} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-429} & & \\\Leftrightarrow & x = \frac{-64}{429} & & \\ & V = \left\{ \frac{-64}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{7})& = & -4x+\frac{7}{12} \\\Leftrightarrow & 21x+4& = & -4x+\frac{7}{12} \\ & & & \text{kgv van noemers 1 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x+ \frac{48}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{+48} & = & \color{red}{-48x} +7 \\\Leftrightarrow & 252x \color{red}{+48} \color{blue}{-48} \color{blue}{+48x} & = & \color{red}{-48x} +7 \color{blue}{+48x} \color{blue}{-48} \\\Leftrightarrow & 252x+48x& = & 7-48 \\\Leftrightarrow & \color{red}{300} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{300} & & \\ & V = \left\{ \frac{-41}{300} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{16}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+176} & = & \color{red}{539x} +14 \\\Leftrightarrow & 924x \color{red}{+176} \color{blue}{-176} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-176} \\\Leftrightarrow & 924x-539x& = & 14-176 \\\Leftrightarrow & \color{red}{385} x& = & -162 \\\Leftrightarrow & x = \frac{-162}{385} & & \\ & V = \left\{ \frac{-162}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 420x+175x& = & 10-84 \\\Leftrightarrow & \color{red}{595} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{595} & & \\ & V = \left\{ \frac{-74}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+108} & = & \color{red}{-360x} +10 \\\Leftrightarrow & -675x \color{red}{+108} \color{blue}{-108} \color{blue}{+360x} & = & \color{red}{-360x} +10 \color{blue}{+360x} \color{blue}{-108} \\\Leftrightarrow & -675x+360x& = & 10-108 \\\Leftrightarrow & \color{red}{-315} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-315} & & \\\Leftrightarrow & x = \frac{14}{45} & & \\ & V = \left\{ \frac{14}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -8x+\frac{9}{7} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+63} & = & \color{red}{-280x} +45 \\\Leftrightarrow & 525x \color{red}{+63} \color{blue}{-63} \color{blue}{+280x} & = & \color{red}{-280x} +45 \color{blue}{+280x} \color{blue}{-63} \\\Leftrightarrow & 525x+280x& = & 45-63 \\\Leftrightarrow & \color{red}{805} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{805} & & \\ & V = \left\{ \frac{-18}{805} \right\} & \\\end{align}\)