Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 30x+\frac{12}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+36} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 990x \color{red}{+36} \color{blue}{-36} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-36} \\\Leftrightarrow & 990x+231x& = & 88-36 \\\Leftrightarrow & \color{red}{1221} x& = & 52 \\\Leftrightarrow & x = \frac{52}{1221} & & \\ & V = \left\{ \frac{52}{1221} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{45x} +25 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +25 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & -120x-45x& = & 25-36 \\\Leftrightarrow & \color{red}{-165} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-165} & & \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{4}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+44} & = & \color{red}{-297x} +54 \\\Leftrightarrow & 990x \color{red}{+44} \color{blue}{-44} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-44} \\\Leftrightarrow & 990x+297x& = & 54-44 \\\Leftrightarrow & \color{red}{1287} x& = & 10 \\\Leftrightarrow & x = \frac{10}{1287} & & \\ & V = \left\{ \frac{10}{1287} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+50} & = & \color{red}{315x} +56 \\\Leftrightarrow & -140x \color{red}{+50} \color{blue}{-50} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-50} \\\Leftrightarrow & -140x-315x& = & 56-50 \\\Leftrightarrow & \color{red}{-455} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-455} & & \\\Leftrightarrow & x = \frac{-6}{455} & & \\ & V = \left\{ \frac{-6}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-40} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 96x \color{red}{-40} \color{blue}{+40} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{+40} \\\Leftrightarrow & 96x+30x& = & 9+40 \\\Leftrightarrow & \color{red}{126} x& = & 49 \\\Leftrightarrow & x = \frac{49}{126} & & \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -9x+\frac{15}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+165} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -693x \color{red}{+165} \color{blue}{-165} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-165} \\\Leftrightarrow & -693x+539x& = & 28-165 \\\Leftrightarrow & \color{red}{-154} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-154} & & \\\Leftrightarrow & x = \frac{137}{154} & & \\ & V = \left\{ \frac{137}{154} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{-270} & = & \color{red}{315x} +28 \\\Leftrightarrow & 1512x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & 1512x-315x& = & 28+270 \\\Leftrightarrow & \color{red}{1197} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1197} & & \\ & V = \left\{ \frac{298}{1197} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{9})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{567x} +81 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{-567x} & = & \color{red}{567x} +81 \color{blue}{-567x} \color{blue}{-56} \\\Leftrightarrow & 504x-567x& = & 81-56 \\\Leftrightarrow & \color{red}{-63} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-63} & & \\\Leftrightarrow & x = \frac{-25}{63} & & \\ & V = \left\{ \frac{-25}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{255} x& = & 4 \\\Leftrightarrow & x = \frac{4}{255} & & \\ & V = \left\{ \frac{4}{255} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 8x+\frac{9}{4} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{64x} +18 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-64x} & = & \color{red}{64x} +18 \color{blue}{-64x} \color{blue}{+21} \\\Leftrightarrow & 168x-64x& = & 18+21 \\\Leftrightarrow & \color{red}{104} x& = & 39 \\\Leftrightarrow & x = \frac{39}{104} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -210x+49x& = & 4-30 \\\Leftrightarrow & \color{red}{-161} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-161} & & \\\Leftrightarrow & x = \frac{26}{161} & & \\ & V = \left\{ \frac{26}{161} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{-24x} +28 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{+24x} & = & \color{red}{-24x} +28 \color{blue}{+24x} \color{blue}{+21} \\\Leftrightarrow & 224x+24x& = & 28+21 \\\Leftrightarrow & \color{red}{248} x& = & 49 \\\Leftrightarrow & x = \frac{49}{248} & & \\ & V = \left\{ \frac{49}{248} \right\} & \\\end{align}\)