Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{11})& = & -2x+\frac{6}{11} \\\Leftrightarrow & -18x-\frac{30}{11}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-30} & = & \color{red}{-22x} +6 \\\Leftrightarrow & -198x \color{red}{-30} \color{blue}{+30} \color{blue}{+22x} & = & \color{red}{-22x} +6 \color{blue}{+22x} \color{blue}{+30} \\\Leftrightarrow & -198x+22x& = & 6+30 \\\Leftrightarrow & \color{red}{-176} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-176} & & \\\Leftrightarrow & x = \frac{-9}{44} & & \\ & V = \left\{ \frac{-9}{44} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+96} & = & \color{red}{308x} +77 \\\Leftrightarrow & 1320x \color{red}{+96} \color{blue}{-96} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{-96} \\\Leftrightarrow & 1320x-308x& = & 77-96 \\\Leftrightarrow & \color{red}{1012} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{1012} & & \\ & V = \left\{ \frac{-19}{1012} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-6} & = & \color{red}{35x} +8 \\\Leftrightarrow & 42x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & 42x-35x& = & 8+6 \\\Leftrightarrow & \color{red}{7} x& = & 14 \\\Leftrightarrow & x = \frac{14}{7} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{28}{9}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{-56} & = & \color{red}{-90x} +27 \\\Leftrightarrow & 504x \color{red}{-56} \color{blue}{+56} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{+56} \\\Leftrightarrow & 504x+90x& = & 27+56 \\\Leftrightarrow & \color{red}{594} x& = & 83 \\\Leftrightarrow & x = \frac{83}{594} & & \\ & V = \left\{ \frac{83}{594} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{4}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-4} & = & \color{red}{27x} +10 \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{+4} \\\Leftrightarrow & -12x-27x& = & 10+4 \\\Leftrightarrow & \color{red}{-39} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-39} & & \\\Leftrightarrow & x = \frac{-14}{39} & & \\ & V = \left\{ \frac{-14}{39} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 20x-\frac{16}{3}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{176}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-176} & = & \color{red}{-99x} +21 \\\Leftrightarrow & 660x \color{red}{-176} \color{blue}{+176} \color{blue}{+99x} & = & \color{red}{-99x} +21 \color{blue}{+99x} \color{blue}{+176} \\\Leftrightarrow & 660x+99x& = & 21+176 \\\Leftrightarrow & \color{red}{759} x& = & 197 \\\Leftrightarrow & x = \frac{197}{759} & & \\ & V = \left\{ \frac{197}{759} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & 2x+\frac{2}{3} \\\Leftrightarrow & -25x+\frac{20}{3}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{+20} & = & \color{red}{6x} +2 \\\Leftrightarrow & -75x \color{red}{+20} \color{blue}{-20} \color{blue}{-6x} & = & \color{red}{6x} +2 \color{blue}{-6x} \color{blue}{-20} \\\Leftrightarrow & -75x-6x& = & 2-20 \\\Leftrightarrow & \color{red}{-81} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-81} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{20}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+140} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -924x \color{red}{+140} \color{blue}{-140} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-140} \\\Leftrightarrow & -924x+385x& = & 22-140 \\\Leftrightarrow & \color{red}{-539} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-539} & & \\\Leftrightarrow & x = \frac{118}{539} & & \\ & V = \left\{ \frac{118}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{8}{7} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+98} & = & \color{red}{-189x} +24 \\\Leftrightarrow & -735x \color{red}{+98} \color{blue}{-98} \color{blue}{+189x} & = & \color{red}{-189x} +24 \color{blue}{+189x} \color{blue}{-98} \\\Leftrightarrow & -735x+189x& = & 24-98 \\\Leftrightarrow & \color{red}{-546} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-546} & & \\\Leftrightarrow & x = \frac{37}{273} & & \\ & V = \left\{ \frac{37}{273} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{400}{ \color{blue}{40} }x- \frac{32}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 400x \color{red}{-32} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 400x \color{red}{-32} \color{blue}{+32} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+32} \\\Leftrightarrow & 400x+280x& = & 35+32 \\\Leftrightarrow & \color{red}{680} x& = & 67 \\\Leftrightarrow & x = \frac{67}{680} & & \\ & V = \left\{ \frac{67}{680} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{15x} +7 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +7 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & 36x-15x& = & 7-8 \\\Leftrightarrow & \color{red}{21} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & 4x+\frac{9}{4} \\\Leftrightarrow & 9x+\frac{9}{5}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{80x} +45 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{-80x} & = & \color{red}{80x} +45 \color{blue}{-80x} \color{blue}{-36} \\\Leftrightarrow & 180x-80x& = & 45-36 \\\Leftrightarrow & \color{red}{100} x& = & 9 \\\Leftrightarrow & x = \frac{9}{100} & & \\ & V = \left\{ \frac{9}{100} \right\} & \\\end{align}\)