Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{10})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -9x+\frac{9}{10}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{50}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{+63} & = & \color{red}{350x} +50 \\\Leftrightarrow & -630x \color{red}{+63} \color{blue}{-63} \color{blue}{-350x} & = & \color{red}{350x} +50 \color{blue}{-350x} \color{blue}{-63} \\\Leftrightarrow & -630x-350x& = & 50-63 \\\Leftrightarrow & \color{red}{-980} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-980} & & \\\Leftrightarrow & x = \frac{13}{980} & & \\ & V = \left\{ \frac{13}{980} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{360}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 360x \color{red}{+96} & = & \color{red}{100x} +45 \\\Leftrightarrow & 360x \color{red}{+96} \color{blue}{-96} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{-96} \\\Leftrightarrow & 360x-100x& = & 45-96 \\\Leftrightarrow & \color{red}{260} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{260} & & \\ & V = \left\{ \frac{-51}{260} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{8})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 14x-\frac{21}{8}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{-189} & = & \color{red}{648x} +80 \\\Leftrightarrow & 1008x \color{red}{-189} \color{blue}{+189} \color{blue}{-648x} & = & \color{red}{648x} +80 \color{blue}{-648x} \color{blue}{+189} \\\Leftrightarrow & 1008x-648x& = & 80+189 \\\Leftrightarrow & \color{red}{360} x& = & 269 \\\Leftrightarrow & x = \frac{269}{360} & & \\ & V = \left\{ \frac{269}{360} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 10x-\frac{8}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-40} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 550x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & 550x+385x& = & 88+40 \\\Leftrightarrow & \color{red}{935} x& = & 128 \\\Leftrightarrow & x = \frac{128}{935} & & \\ & V = \left\{ \frac{128}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-90} & = & \color{red}{165x} +110 \\\Leftrightarrow & 792x \color{red}{-90} \color{blue}{+90} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+90} \\\Leftrightarrow & 792x-165x& = & 110+90 \\\Leftrightarrow & \color{red}{627} x& = & 200 \\\Leftrightarrow & x = \frac{200}{627} & & \\ & V = \left\{ \frac{200}{627} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-25x} +2 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -60x+25x& = & 2-12 \\\Leftrightarrow & \color{red}{-35} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-35} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -14x-\frac{35}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x- \frac{175}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{-175} & = & \color{red}{165x} +66 \\\Leftrightarrow & -770x \color{red}{-175} \color{blue}{+175} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{+175} \\\Leftrightarrow & -770x-165x& = & 66+175 \\\Leftrightarrow & \color{red}{-935} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-935} & & \\\Leftrightarrow & x = \frac{-241}{935} & & \\ & V = \left\{ \frac{-241}{935} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-66} & = & \color{red}{231x} +35 \\\Leftrightarrow & 770x \color{red}{-66} \color{blue}{+66} \color{blue}{-231x} & = & \color{red}{231x} +35 \color{blue}{-231x} \color{blue}{+66} \\\Leftrightarrow & 770x-231x& = & 35+66 \\\Leftrightarrow & \color{red}{539} x& = & 101 \\\Leftrightarrow & x = \frac{101}{539} & & \\ & V = \left\{ \frac{101}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -4x-\frac{10}{11}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-10} & = & \color{red}{-99x} +4 \\\Leftrightarrow & -44x \color{red}{-10} \color{blue}{+10} \color{blue}{+99x} & = & \color{red}{-99x} +4 \color{blue}{+99x} \color{blue}{+10} \\\Leftrightarrow & -44x+99x& = & 4+10 \\\Leftrightarrow & \color{red}{55} x& = & 14 \\\Leftrightarrow & x = \frac{14}{55} & & \\ & V = \left\{ \frac{14}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-16} & = & \color{red}{42x} +27 \\\Leftrightarrow & 60x \color{red}{-16} \color{blue}{+16} \color{blue}{-42x} & = & \color{red}{42x} +27 \color{blue}{-42x} \color{blue}{+16} \\\Leftrightarrow & 60x-42x& = & 27+16 \\\Leftrightarrow & \color{red}{18} x& = & 43 \\\Leftrightarrow & x = \frac{43}{18} & & \\ & V = \left\{ \frac{43}{18} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 50-84 \\\Leftrightarrow & \color{red}{-595} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-595} & & \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+60} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -840x \color{red}{+60} \color{blue}{-60} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-60} \\\Leftrightarrow & -840x+350x& = & 63-60 \\\Leftrightarrow & \color{red}{-490} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-490} & & \\\Leftrightarrow & x = \frac{-3}{490} & & \\ & V = \left\{ \frac{-3}{490} \right\} & \\\end{align}\)