Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & 3x+\frac{5}{8} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-192}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -192x \color{red}{+160} & = & \color{red}{72x} +15 \\\Leftrightarrow & -192x \color{red}{+160} \color{blue}{-160} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{-160} \\\Leftrightarrow & -192x-72x& = & 15-160 \\\Leftrightarrow & \color{red}{-264} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-264} & & \\\Leftrightarrow & x = \frac{145}{264} & & \\ & V = \left\{ \frac{145}{264} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{9})& = & -3x+\frac{9}{7} \\\Leftrightarrow & 35x+\frac{28}{9}& = & -3x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{2205}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 2205x \color{red}{+196} & = & \color{red}{-189x} +81 \\\Leftrightarrow & 2205x \color{red}{+196} \color{blue}{-196} \color{blue}{+189x} & = & \color{red}{-189x} +81 \color{blue}{+189x} \color{blue}{-196} \\\Leftrightarrow & 2205x+189x& = & 81-196 \\\Leftrightarrow & \color{red}{2394} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{2394} & & \\ & V = \left\{ \frac{-115}{2394} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+6} & = & \color{red}{49x} +4 \\\Leftrightarrow & 42x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 42x-49x& = & 4-6 \\\Leftrightarrow & \color{red}{-7} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-7} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & -300x+70x& = & 3-48 \\\Leftrightarrow & \color{red}{-230} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-230} & & \\\Leftrightarrow & x = \frac{9}{46} & & \\ & V = \left\{ \frac{9}{46} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-150} & = & \color{red}{-175x} +56 \\\Leftrightarrow & -420x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & -420x+175x& = & 56+150 \\\Leftrightarrow & \color{red}{-245} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-245} & & \\\Leftrightarrow & x = \frac{-206}{245} & & \\ & V = \left\{ \frac{-206}{245} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{25}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+25} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 165x \color{red}{+25} \color{blue}{-25} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-25} \\\Leftrightarrow & 165x+77x& = & 2-25 \\\Leftrightarrow & \color{red}{242} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{242} & & \\ & V = \left\{ \frac{-23}{242} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{12})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x-\frac{35}{12}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-35} & = & \color{red}{-96x} +8 \\\Leftrightarrow & -252x \color{red}{-35} \color{blue}{+35} \color{blue}{+96x} & = & \color{red}{-96x} +8 \color{blue}{+96x} \color{blue}{+35} \\\Leftrightarrow & -252x+96x& = & 8+35 \\\Leftrightarrow & \color{red}{-156} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-156} & & \\\Leftrightarrow & x = \frac{-43}{156} & & \\ & V = \left\{ \frac{-43}{156} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -14x+\frac{28}{9}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-882}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -882x \color{red}{+196} & = & \color{red}{315x} +27 \\\Leftrightarrow & -882x \color{red}{+196} \color{blue}{-196} \color{blue}{-315x} & = & \color{red}{315x} +27 \color{blue}{-315x} \color{blue}{-196} \\\Leftrightarrow & -882x-315x& = & 27-196 \\\Leftrightarrow & \color{red}{-1197} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-1197} & & \\\Leftrightarrow & x = \frac{169}{1197} & & \\ & V = \left\{ \frac{169}{1197} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{20}{3}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-20} & = & \color{red}{-15x} +2 \\\Leftrightarrow & 36x \color{red}{-20} \color{blue}{+20} \color{blue}{+15x} & = & \color{red}{-15x} +2 \color{blue}{+15x} \color{blue}{+20} \\\Leftrightarrow & 36x+15x& = & 2+20 \\\Leftrightarrow & \color{red}{51} x& = & 22 \\\Leftrightarrow & x = \frac{22}{51} & & \\ & V = \left\{ \frac{22}{51} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{5})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -35x-\frac{14}{5}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-700}{ \color{blue}{20} }x- \frac{56}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -700x \color{red}{-56} & = & \color{red}{-180x} +45 \\\Leftrightarrow & -700x \color{red}{-56} \color{blue}{+56} \color{blue}{+180x} & = & \color{red}{-180x} +45 \color{blue}{+180x} \color{blue}{+56} \\\Leftrightarrow & -700x+180x& = & 45+56 \\\Leftrightarrow & \color{red}{-520} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-520} & & \\\Leftrightarrow & x = \frac{-101}{520} & & \\ & V = \left\{ \frac{-101}{520} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 60x+25x& = & 8-12 \\\Leftrightarrow & \color{red}{85} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{85} & & \\ & V = \left\{ \frac{-4}{85} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{4})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -35x-\frac{35}{4}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1260}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1260x \color{red}{-315} & = & \color{red}{-324x} +16 \\\Leftrightarrow & -1260x \color{red}{-315} \color{blue}{+315} \color{blue}{+324x} & = & \color{red}{-324x} +16 \color{blue}{+324x} \color{blue}{+315} \\\Leftrightarrow & -1260x+324x& = & 16+315 \\\Leftrightarrow & \color{red}{-936} x& = & 331 \\\Leftrightarrow & x = \frac{331}{-936} & & \\\Leftrightarrow & x = \frac{-331}{936} & & \\ & V = \left\{ \frac{-331}{936} \right\} & \\\end{align}\)