Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{-50x} +7 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +7 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 120x+50x& = & 7+24 \\\Leftrightarrow & \color{red}{170} x& = & 31 \\\Leftrightarrow & x = \frac{31}{170} & & \\ & V = \left\{ \frac{31}{170} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{10})& = & 4x+\frac{5}{3} \\\Leftrightarrow & 9x-\frac{9}{10}& = & 4x+\frac{5}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{270}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{50}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 270x \color{red}{-27} & = & \color{red}{120x} +50 \\\Leftrightarrow & 270x \color{red}{-27} \color{blue}{+27} \color{blue}{-120x} & = & \color{red}{120x} +50 \color{blue}{-120x} \color{blue}{+27} \\\Leftrightarrow & 270x-120x& = & 50+27 \\\Leftrightarrow & \color{red}{150} x& = & 77 \\\Leftrightarrow & x = \frac{77}{150} & & \\ & V = \left\{ \frac{77}{150} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 30x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{5} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 9x+\frac{3}{5} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 9x+\frac{3}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{27}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{405x} +27 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{-405x} & = & \color{red}{405x} +27 \color{blue}{-405x} \color{blue}{-40} \\\Leftrightarrow & 360x-405x& = & 27-40 \\\Leftrightarrow & \color{red}{-45} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-45} & & \\\Leftrightarrow & x = \frac{13}{45} & & \\ & V = \left\{ \frac{13}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 210x+175x& = & 30+84 \\\Leftrightarrow & \color{red}{385} x& = & 114 \\\Leftrightarrow & x = \frac{114}{385} & & \\ & V = \left\{ \frac{114}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{8}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{56}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-56} & = & \color{red}{385x} +110 \\\Leftrightarrow & 462x \color{red}{-56} \color{blue}{+56} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{+56} \\\Leftrightarrow & 462x-385x& = & 110+56 \\\Leftrightarrow & \color{red}{77} x& = & 166 \\\Leftrightarrow & x = \frac{166}{77} & & \\ & V = \left\{ \frac{166}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & -4x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-84} & = & \color{red}{-140x} +45 \\\Leftrightarrow & -525x \color{red}{-84} \color{blue}{+84} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{+84} \\\Leftrightarrow & -525x+140x& = & 45+84 \\\Leftrightarrow & \color{red}{-385} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-385} & & \\\Leftrightarrow & x = \frac{-129}{385} & & \\ & V = \left\{ \frac{-129}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-210} & = & \color{red}{539x} +110 \\\Leftrightarrow & 1848x \color{red}{-210} \color{blue}{+210} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+210} \\\Leftrightarrow & 1848x-539x& = & 110+210 \\\Leftrightarrow & \color{red}{1309} x& = & 320 \\\Leftrightarrow & x = \frac{320}{1309} & & \\ & V = \left\{ \frac{320}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{5})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+63} & = & \color{red}{-70x} +50 \\\Leftrightarrow & 525x \color{red}{+63} \color{blue}{-63} \color{blue}{+70x} & = & \color{red}{-70x} +50 \color{blue}{+70x} \color{blue}{-63} \\\Leftrightarrow & 525x+70x& = & 50-63 \\\Leftrightarrow & \color{red}{595} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{595} & & \\ & V = \left\{ \frac{-13}{595} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-126} & = & \color{red}{-539x} +88 \\\Leftrightarrow & -2310x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & -2310x+539x& = & 88+126 \\\Leftrightarrow & \color{red}{-1771} x& = & 214 \\\Leftrightarrow & x = \frac{214}{-1771} & & \\\Leftrightarrow & x = \frac{-214}{1771} & & \\ & V = \left\{ \frac{-214}{1771} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 9x+\frac{12}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{792}{ \color{blue}{88} }x+ \frac{96}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 792x \color{red}{+96} & = & \color{red}{-440x} +77 \\\Leftrightarrow & 792x \color{red}{+96} \color{blue}{-96} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{-96} \\\Leftrightarrow & 792x+440x& = & 77-96 \\\Leftrightarrow & \color{red}{1232} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{1232} & & \\ & V = \left\{ \frac{-19}{1232} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+6} & = & \color{red}{-35x} +3 \\\Leftrightarrow & -63x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -63x+35x& = & 3-6 \\\Leftrightarrow & \color{red}{-28} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-28} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)