Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{9})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-4} & = & \color{red}{-27x} +10 \\\Leftrightarrow & -72x \color{red}{-4} \color{blue}{+4} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{+4} \\\Leftrightarrow & -72x+27x& = & 10+4 \\\Leftrightarrow & \color{red}{-45} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-45} & & \\\Leftrightarrow & x = \frac{-14}{45} & & \\ & V = \left\{ \frac{-14}{45} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{12}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{-12} & = & \color{red}{55x} +6 \\\Leftrightarrow & -264x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & -264x-55x& = & 6+12 \\\Leftrightarrow & \color{red}{-319} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-319} & & \\\Leftrightarrow & x = \frac{-18}{319} & & \\ & V = \left\{ \frac{-18}{319} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{+36} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 660x \color{red}{+36} \color{blue}{-36} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{-36} \\\Leftrightarrow & 660x+154x& = & 77-36 \\\Leftrightarrow & \color{red}{814} x& = & 41 \\\Leftrightarrow & x = \frac{41}{814} & & \\ & V = \left\{ \frac{41}{814} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 6x-\frac{8}{7}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-40} & = & \color{red}{-175x} +21 \\\Leftrightarrow & 210x \color{red}{-40} \color{blue}{+40} \color{blue}{+175x} & = & \color{red}{-175x} +21 \color{blue}{+175x} \color{blue}{+40} \\\Leftrightarrow & 210x+175x& = & 21+40 \\\Leftrightarrow & \color{red}{385} x& = & 61 \\\Leftrightarrow & x = \frac{61}{385} & & \\ & V = \left\{ \frac{61}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+48} & = & \color{red}{100x} +35 \\\Leftrightarrow & 480x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & 480x-100x& = & 35-48 \\\Leftrightarrow & \color{red}{380} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{380} & & \\ & V = \left\{ \frac{-13}{380} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 20x+\frac{10}{11}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+10} & = & \color{red}{99x} +5 \\\Leftrightarrow & 220x \color{red}{+10} \color{blue}{-10} \color{blue}{-99x} & = & \color{red}{99x} +5 \color{blue}{-99x} \color{blue}{-10} \\\Leftrightarrow & 220x-99x& = & 5-10 \\\Leftrightarrow & \color{red}{121} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{121} & & \\ & V = \left\{ \frac{-5}{121} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{105} x& = & 86 \\\Leftrightarrow & x = \frac{86}{105} & & \\ & V = \left\{ \frac{86}{105} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & -2x+\frac{9}{2} \\\Leftrightarrow & -18x+\frac{18}{11}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{-44x} +99 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{+44x} & = & \color{red}{-44x} +99 \color{blue}{+44x} \color{blue}{-36} \\\Leftrightarrow & -396x+44x& = & 99-36 \\\Leftrightarrow & \color{red}{-352} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-352} & & \\\Leftrightarrow & x = \frac{-63}{352} & & \\ & V = \left\{ \frac{-63}{352} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{4})& = & -8x+\frac{3}{4} \\\Leftrightarrow & 21x+\frac{21}{4}& = & -8x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x+ \frac{21}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{+21} & = & \color{red}{-32x} +3 \\\Leftrightarrow & 84x \color{red}{+21} \color{blue}{-21} \color{blue}{+32x} & = & \color{red}{-32x} +3 \color{blue}{+32x} \color{blue}{-21} \\\Leftrightarrow & 84x+32x& = & 3-21 \\\Leftrightarrow & \color{red}{116} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{116} & & \\\Leftrightarrow & x = \frac{-9}{58} & & \\ & V = \left\{ \frac{-9}{58} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{11})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{+30} & = & \color{red}{297x} +110 \\\Leftrightarrow & 132x \color{red}{+30} \color{blue}{-30} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{-30} \\\Leftrightarrow & 132x-297x& = & 110-30 \\\Leftrightarrow & \color{red}{-165} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-165} & & \\\Leftrightarrow & x = \frac{-16}{33} & & \\ & V = \left\{ \frac{-16}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{5})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{21}{5}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{63}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+63} & = & \color{red}{-30x} +40 \\\Leftrightarrow & 315x \color{red}{+63} \color{blue}{-63} \color{blue}{+30x} & = & \color{red}{-30x} +40 \color{blue}{+30x} \color{blue}{-63} \\\Leftrightarrow & 315x+30x& = & 40-63 \\\Leftrightarrow & \color{red}{345} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{345} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & 2x+\frac{9}{8} \\\Leftrightarrow & -28x+\frac{21}{11}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{168}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+168} & = & \color{red}{176x} +99 \\\Leftrightarrow & -2464x \color{red}{+168} \color{blue}{-168} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-168} \\\Leftrightarrow & -2464x-176x& = & 99-168 \\\Leftrightarrow & \color{red}{-2640} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-2640} & & \\\Leftrightarrow & x = \frac{23}{880} & & \\ & V = \left\{ \frac{23}{880} \right\} & \\\end{align}\)