Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{315x} +40 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-84} \\\Leftrightarrow & -280x-315x& = & 40-84 \\\Leftrightarrow & \color{red}{-595} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-595} & & \\\Leftrightarrow & x = \frac{44}{595} & & \\ & V = \left\{ \frac{44}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{2})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{15}{2}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-45} & = & \color{red}{-42x} +20 \\\Leftrightarrow & 120x \color{red}{-45} \color{blue}{+45} \color{blue}{+42x} & = & \color{red}{-42x} +20 \color{blue}{+42x} \color{blue}{+45} \\\Leftrightarrow & 120x+42x& = & 20+45 \\\Leftrightarrow & \color{red}{162} x& = & 65 \\\Leftrightarrow & x = \frac{65}{162} & & \\ & V = \left\{ \frac{65}{162} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{2})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -15x-\frac{25}{2}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{-225} & = & \color{red}{-144x} +16 \\\Leftrightarrow & -270x \color{red}{-225} \color{blue}{+225} \color{blue}{+144x} & = & \color{red}{-144x} +16 \color{blue}{+144x} \color{blue}{+225} \\\Leftrightarrow & -270x+144x& = & 16+225 \\\Leftrightarrow & \color{red}{-126} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-126} & & \\\Leftrightarrow & x = \frac{-241}{126} & & \\ & V = \left\{ \frac{-241}{126} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-6} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -42x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -42x+49x& = & 4+6 \\\Leftrightarrow & \color{red}{7} x& = & 10 \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+176} & = & \color{red}{539x} +14 \\\Leftrightarrow & -1540x \color{red}{+176} \color{blue}{-176} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-176} \\\Leftrightarrow & -1540x-539x& = & 14-176 \\\Leftrightarrow & \color{red}{-2079} x& = & -162 \\\Leftrightarrow & x = \frac{-162}{-2079} & & \\\Leftrightarrow & x = \frac{6}{77} & & \\ & V = \left\{ \frac{6}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{-63} & = & \color{red}{-72x} +16 \\\Leftrightarrow & -336x \color{red}{-63} \color{blue}{+63} \color{blue}{+72x} & = & \color{red}{-72x} +16 \color{blue}{+72x} \color{blue}{+63} \\\Leftrightarrow & -336x+72x& = & 16+63 \\\Leftrightarrow & \color{red}{-264} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-264} & & \\\Leftrightarrow & x = \frac{-79}{264} & & \\ & V = \left\{ \frac{-79}{264} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{8})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{9}{8}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{+27} & = & \color{red}{-168x} +16 \\\Leftrightarrow & -144x \color{red}{+27} \color{blue}{-27} \color{blue}{+168x} & = & \color{red}{-168x} +16 \color{blue}{+168x} \color{blue}{-27} \\\Leftrightarrow & -144x+168x& = & 16-27 \\\Leftrightarrow & \color{red}{24} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{24} & & \\ & V = \left\{ \frac{-11}{24} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -630x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -630x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{-455} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-455} & & \\\Leftrightarrow & x = \frac{-99}{455} & & \\ & V = \left\{ \frac{-99}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -10x+\frac{15}{2}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+45} & = & \color{red}{-42x} +14 \\\Leftrightarrow & -60x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +14 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & -60x+42x& = & 14-45 \\\Leftrightarrow & \color{red}{-18} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-18} & & \\\Leftrightarrow & x = \frac{31}{18} & & \\ & V = \left\{ \frac{31}{18} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+36} & = & \color{red}{231x} +22 \\\Leftrightarrow & -198x \color{red}{+36} \color{blue}{-36} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-36} \\\Leftrightarrow & -198x-231x& = & 22-36 \\\Leftrightarrow & \color{red}{-429} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-429} & & \\\Leftrightarrow & x = \frac{14}{429} & & \\ & V = \left\{ \frac{14}{429} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 30x-\frac{12}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-132} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 2310x \color{red}{-132} \color{blue}{+132} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+132} \\\Leftrightarrow & 2310x+539x& = & 42+132 \\\Leftrightarrow & \color{red}{2849} x& = & 174 \\\Leftrightarrow & x = \frac{174}{2849} & & \\ & V = \left\{ \frac{174}{2849} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{15}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-135} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -1980x \color{red}{-135} \color{blue}{+135} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+135} \\\Leftrightarrow & -1980x+693x& = & 110+135 \\\Leftrightarrow & \color{red}{-1287} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-1287} & & \\\Leftrightarrow & x = \frac{-245}{1287} & & \\ & V = \left\{ \frac{-245}{1287} \right\} & \\\end{align}\)