Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-198} & = & \color{red}{-165x} +25 \\\Leftrightarrow & -990x \color{red}{-198} \color{blue}{+198} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{+198} \\\Leftrightarrow & -990x+165x& = & 25+198 \\\Leftrightarrow & \color{red}{-825} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-825} & & \\\Leftrightarrow & x = \frac{-223}{825} & & \\ & V = \left\{ \frac{-223}{825} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 18x+\frac{18}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x+ \frac{162}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{+162} & = & \color{red}{441x} +70 \\\Leftrightarrow & 1134x \color{red}{+162} \color{blue}{-162} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-162} \\\Leftrightarrow & 1134x-441x& = & 70-162 \\\Leftrightarrow & \color{red}{693} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{693} & & \\ & V = \left\{ \frac{-92}{693} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{+40} \\\Leftrightarrow & -440x+308x& = & 33+40 \\\Leftrightarrow & \color{red}{-132} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-132} & & \\\Leftrightarrow & x = \frac{-73}{132} & & \\ & V = \left\{ \frac{-73}{132} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & 4x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{6}{11}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-30} & = & \color{red}{220x} +44 \\\Leftrightarrow & 825x \color{red}{-30} \color{blue}{+30} \color{blue}{-220x} & = & \color{red}{220x} +44 \color{blue}{-220x} \color{blue}{+30} \\\Leftrightarrow & 825x-220x& = & 44+30 \\\Leftrightarrow & \color{red}{605} x& = & 74 \\\Leftrightarrow & x = \frac{74}{605} & & \\ & V = \left\{ \frac{74}{605} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{3})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -16x+\frac{16}{3}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+176} & = & \color{red}{231x} +12 \\\Leftrightarrow & -528x \color{red}{+176} \color{blue}{-176} \color{blue}{-231x} & = & \color{red}{231x} +12 \color{blue}{-231x} \color{blue}{-176} \\\Leftrightarrow & -528x-231x& = & 12-176 \\\Leftrightarrow & \color{red}{-759} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{-759} & & \\\Leftrightarrow & x = \frac{164}{759} & & \\ & V = \left\{ \frac{164}{759} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{5})& = & 9x+\frac{9}{8} \\\Leftrightarrow & -8x-\frac{8}{5}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x- \frac{64}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{-64} & = & \color{red}{360x} +45 \\\Leftrightarrow & -320x \color{red}{-64} \color{blue}{+64} \color{blue}{-360x} & = & \color{red}{360x} +45 \color{blue}{-360x} \color{blue}{+64} \\\Leftrightarrow & -320x-360x& = & 45+64 \\\Leftrightarrow & \color{red}{-680} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-680} & & \\\Leftrightarrow & x = \frac{-109}{680} & & \\ & V = \left\{ \frac{-109}{680} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-252}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -252x \color{red}{-36} & = & \color{red}{-294x} +35 \\\Leftrightarrow & -252x \color{red}{-36} \color{blue}{+36} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+36} \\\Leftrightarrow & -252x+294x& = & 35+36 \\\Leftrightarrow & \color{red}{42} x& = & 71 \\\Leftrightarrow & x = \frac{71}{42} & & \\ & V = \left\{ \frac{71}{42} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 45x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 45x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{80} x& = & 18 \\\Leftrightarrow & x = \frac{18}{80} & & \\\Leftrightarrow & x = \frac{9}{40} & & \\ & V = \left\{ \frac{9}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{4})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -14x-\frac{21}{4}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-56}{ \color{blue}{4} }x- \frac{21}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -56x \color{red}{-21} & = & \color{red}{-20x} +3 \\\Leftrightarrow & -56x \color{red}{-21} \color{blue}{+21} \color{blue}{+20x} & = & \color{red}{-20x} +3 \color{blue}{+20x} \color{blue}{+21} \\\Leftrightarrow & -56x+20x& = & 3+21 \\\Leftrightarrow & \color{red}{-36} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-36} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -9x-\frac{15}{7}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x- \frac{150}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-350x} +49 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+350x} & = & \color{red}{-350x} +49 \color{blue}{+350x} \color{blue}{+150} \\\Leftrightarrow & -630x+350x& = & 49+150 \\\Leftrightarrow & \color{red}{-280} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-280} & & \\\Leftrightarrow & x = \frac{-199}{280} & & \\ & V = \left\{ \frac{-199}{280} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{3})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+245} & = & \color{red}{-189x} +9 \\\Leftrightarrow & -735x \color{red}{+245} \color{blue}{-245} \color{blue}{+189x} & = & \color{red}{-189x} +9 \color{blue}{+189x} \color{blue}{-245} \\\Leftrightarrow & -735x+189x& = & 9-245 \\\Leftrightarrow & \color{red}{-546} x& = & -236 \\\Leftrightarrow & x = \frac{-236}{-546} & & \\\Leftrightarrow & x = \frac{118}{273} & & \\ & V = \left\{ \frac{118}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{-595} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-595} & & \\\Leftrightarrow & x = \frac{-134}{595} & & \\ & V = \left\{ \frac{-134}{595} \right\} & \\\end{align}\)