Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{4})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{9}{4}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+99} & = & \color{red}{-220x} +32 \\\Leftrightarrow & 528x \color{red}{+99} \color{blue}{-99} \color{blue}{+220x} & = & \color{red}{-220x} +32 \color{blue}{+220x} \color{blue}{-99} \\\Leftrightarrow & 528x+220x& = & 32-99 \\\Leftrightarrow & \color{red}{748} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{748} & & \\ & V = \left\{ \frac{-67}{748} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{7}{6} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{12x} +7 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +7 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & 126x-12x& = & 7+28 \\\Leftrightarrow & \color{red}{114} x& = & 35 \\\Leftrightarrow & x = \frac{35}{114} & & \\ & V = \left\{ \frac{35}{114} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+36} & = & \color{red}{-110x} +55 \\\Leftrightarrow & -264x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & -264x+110x& = & 55-36 \\\Leftrightarrow & \color{red}{-154} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-154} & & \\\Leftrightarrow & x = \frac{-19}{154} & & \\ & V = \left\{ \frac{-19}{154} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-300} & = & \color{red}{-350x} +21 \\\Leftrightarrow & 840x \color{red}{-300} \color{blue}{+300} \color{blue}{+350x} & = & \color{red}{-350x} +21 \color{blue}{+350x} \color{blue}{+300} \\\Leftrightarrow & 840x+350x& = & 21+300 \\\Leftrightarrow & \color{red}{1190} x& = & 321 \\\Leftrightarrow & x = \frac{321}{1190} & & \\ & V = \left\{ \frac{321}{1190} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{35}{2}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{294}{ \color{blue}{14} }x+ \frac{245}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 294x \color{red}{+245} & = & \color{red}{-28x} +12 \\\Leftrightarrow & 294x \color{red}{+245} \color{blue}{-245} \color{blue}{+28x} & = & \color{red}{-28x} +12 \color{blue}{+28x} \color{blue}{-245} \\\Leftrightarrow & 294x+28x& = & 12-245 \\\Leftrightarrow & \color{red}{322} x& = & -233 \\\Leftrightarrow & x = \frac{-233}{322} & & \\ & V = \left\{ \frac{-233}{322} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{9})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -35x+\frac{14}{9}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{+154} & = & \color{red}{297x} +18 \\\Leftrightarrow & -3465x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & -3465x-297x& = & 18-154 \\\Leftrightarrow & \color{red}{-3762} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-3762} & & \\\Leftrightarrow & x = \frac{68}{1881} & & \\ & V = \left\{ \frac{68}{1881} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 10x-\frac{8}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-8} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 70x \color{red}{-8} \color{blue}{+8} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{+8} \\\Leftrightarrow & 70x+21x& = & 3+8 \\\Leftrightarrow & \color{red}{91} x& = & 11 \\\Leftrightarrow & x = \frac{11}{91} & & \\ & V = \left\{ \frac{11}{91} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{-12} & = & \color{red}{70x} +63 \\\Leftrightarrow & -56x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -56x-70x& = & 63+12 \\\Leftrightarrow & \color{red}{-126} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-126} & & \\\Leftrightarrow & x = \frac{-25}{42} & & \\ & V = \left\{ \frac{-25}{42} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+100} & = & \color{red}{120x} +6 \\\Leftrightarrow & -225x \color{red}{+100} \color{blue}{-100} \color{blue}{-120x} & = & \color{red}{120x} +6 \color{blue}{-120x} \color{blue}{-100} \\\Leftrightarrow & -225x-120x& = & 6-100 \\\Leftrightarrow & \color{red}{-345} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-345} & & \\\Leftrightarrow & x = \frac{94}{345} & & \\ & V = \left\{ \frac{94}{345} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 210x+175x& = & 20-84 \\\Leftrightarrow & \color{red}{385} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{385} & & \\ & V = \left\{ \frac{-64}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{-315x} +40 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -1350x+315x& = & 40-108 \\\Leftrightarrow & \color{red}{-1035} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1035} & & \\\Leftrightarrow & x = \frac{68}{1035} & & \\ & V = \left\{ \frac{68}{1035} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{21}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{308}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 308x \color{red}{-42} & = & \color{red}{198x} +99 \\\Leftrightarrow & 308x \color{red}{-42} \color{blue}{+42} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{+42} \\\Leftrightarrow & 308x-198x& = & 99+42 \\\Leftrightarrow & \color{red}{110} x& = & 141 \\\Leftrightarrow & x = \frac{141}{110} & & \\ & V = \left\{ \frac{141}{110} \right\} & \\\end{align}\)