Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x-\frac{24}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-168} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -2310x \color{red}{-168} \color{blue}{+168} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+168} \\\Leftrightarrow & -2310x+539x& = & 110+168 \\\Leftrightarrow & \color{red}{-1771} x& = & 278 \\\Leftrightarrow & x = \frac{278}{-1771} & & \\\Leftrightarrow & x = \frac{-278}{1771} & & \\ & V = \left\{ \frac{-278}{1771} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-220} & = & \color{red}{66x} +18 \\\Leftrightarrow & 495x \color{red}{-220} \color{blue}{+220} \color{blue}{-66x} & = & \color{red}{66x} +18 \color{blue}{-66x} \color{blue}{+220} \\\Leftrightarrow & 495x-66x& = & 18+220 \\\Leftrightarrow & \color{red}{429} x& = & 238 \\\Leftrightarrow & x = \frac{238}{429} & & \\ & V = \left\{ \frac{238}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -2x+\frac{5}{6} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+63} & = & \color{red}{-12x} +5 \\\Leftrightarrow & 126x \color{red}{+63} \color{blue}{-63} \color{blue}{+12x} & = & \color{red}{-12x} +5 \color{blue}{+12x} \color{blue}{-63} \\\Leftrightarrow & 126x+12x& = & 5-63 \\\Leftrightarrow & \color{red}{138} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{138} & & \\\Leftrightarrow & x = \frac{-29}{69} & & \\ & V = \left\{ \frac{-29}{69} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{200x} +48 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{+105} \\\Leftrightarrow & 840x-200x& = & 48+105 \\\Leftrightarrow & \color{red}{640} x& = & 153 \\\Leftrightarrow & x = \frac{153}{640} & & \\ & V = \left\{ \frac{153}{640} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & 5x+\frac{7}{9} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-270} & = & \color{red}{315x} +49 \\\Leftrightarrow & -756x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & -756x-315x& = & 49+270 \\\Leftrightarrow & \color{red}{-1071} x& = & 319 \\\Leftrightarrow & x = \frac{319}{-1071} & & \\\Leftrightarrow & x = \frac{-319}{1071} & & \\ & V = \left\{ \frac{-319}{1071} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{-175x} +40 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{-168} \\\Leftrightarrow & -840x+175x& = & 40-168 \\\Leftrightarrow & \color{red}{-665} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-665} & & \\\Leftrightarrow & x = \frac{128}{665} & & \\ & V = \left\{ \frac{128}{665} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{12})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{25}{12}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{540}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{+125} & = & \color{red}{540x} +72 \\\Leftrightarrow & -1200x \color{red}{+125} \color{blue}{-125} \color{blue}{-540x} & = & \color{red}{540x} +72 \color{blue}{-540x} \color{blue}{-125} \\\Leftrightarrow & -1200x-540x& = & 72-125 \\\Leftrightarrow & \color{red}{-1740} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-1740} & & \\\Leftrightarrow & x = \frac{53}{1740} & & \\ & V = \left\{ \frac{53}{1740} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{7})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{20}{7}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-60} & = & \color{red}{84x} +56 \\\Leftrightarrow & -315x \color{red}{-60} \color{blue}{+60} \color{blue}{-84x} & = & \color{red}{84x} +56 \color{blue}{-84x} \color{blue}{+60} \\\Leftrightarrow & -315x-84x& = & 56+60 \\\Leftrightarrow & \color{red}{-399} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-399} & & \\\Leftrightarrow & x = \frac{-116}{399} & & \\ & V = \left\{ \frac{-116}{399} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & 504x+315x& = & 18-56 \\\Leftrightarrow & \color{red}{819} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{819} & & \\ & V = \left\{ \frac{-38}{819} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -16x-\frac{8}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-8} & = & \color{red}{49x} +6 \\\Leftrightarrow & -112x \color{red}{-8} \color{blue}{+8} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+8} \\\Leftrightarrow & -112x-49x& = & 6+8 \\\Leftrightarrow & \color{red}{-161} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-161} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-120}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-150x} +35 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+150x} & = & \color{red}{-150x} +35 \color{blue}{+150x} \color{blue}{-24} \\\Leftrightarrow & -120x+150x& = & 35-24 \\\Leftrightarrow & \color{red}{30} x& = & 11 \\\Leftrightarrow & x = \frac{11}{30} & & \\ & V = \left\{ \frac{11}{30} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +56 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 56-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1001} & & \\\Leftrightarrow & x = \frac{10}{1001} & & \\ & V = \left\{ \frac{10}{1001} \right\} & \\\end{align}\)