Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{3})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+200} & = & \color{red}{210x} +27 \\\Leftrightarrow & -600x \color{red}{+200} \color{blue}{-200} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{-200} \\\Leftrightarrow & -600x-210x& = & 27-200 \\\Leftrightarrow & \color{red}{-810} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-810} & & \\\Leftrightarrow & x = \frac{173}{810} & & \\ & V = \left\{ \frac{173}{810} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{8})& = & 8x+\frac{4}{11} \\\Leftrightarrow & -15x-\frac{25}{8}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1320}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1320x \color{red}{-275} & = & \color{red}{704x} +32 \\\Leftrightarrow & -1320x \color{red}{-275} \color{blue}{+275} \color{blue}{-704x} & = & \color{red}{704x} +32 \color{blue}{-704x} \color{blue}{+275} \\\Leftrightarrow & -1320x-704x& = & 32+275 \\\Leftrightarrow & \color{red}{-2024} x& = & 307 \\\Leftrightarrow & x = \frac{307}{-2024} & & \\\Leftrightarrow & x = \frac{-307}{2024} & & \\ & V = \left\{ \frac{-307}{2024} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+50} & = & \color{red}{-280x} +42 \\\Leftrightarrow & -525x \color{red}{+50} \color{blue}{-50} \color{blue}{+280x} & = & \color{red}{-280x} +42 \color{blue}{+280x} \color{blue}{-50} \\\Leftrightarrow & -525x+280x& = & 42-50 \\\Leftrightarrow & \color{red}{-245} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-245} & & \\\Leftrightarrow & x = \frac{8}{245} & & \\ & V = \left\{ \frac{8}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{11})& = & -8x+\frac{5}{12} \\\Leftrightarrow & 21x-\frac{14}{11}& = & -8x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2772}{ \color{blue}{132} }x- \frac{168}{ \color{blue}{132} })& = & (\frac{-1056}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2772x \color{red}{-168} & = & \color{red}{-1056x} +55 \\\Leftrightarrow & 2772x \color{red}{-168} \color{blue}{+168} \color{blue}{+1056x} & = & \color{red}{-1056x} +55 \color{blue}{+1056x} \color{blue}{+168} \\\Leftrightarrow & 2772x+1056x& = & 55+168 \\\Leftrightarrow & \color{red}{3828} x& = & 223 \\\Leftrightarrow & x = \frac{223}{3828} & & \\ & V = \left\{ \frac{223}{3828} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{11})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -21x-\frac{28}{11}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-56} & = & \color{red}{176x} +99 \\\Leftrightarrow & -462x \color{red}{-56} \color{blue}{+56} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{+56} \\\Leftrightarrow & -462x-176x& = & 99+56 \\\Leftrightarrow & \color{red}{-638} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-638} & & \\\Leftrightarrow & x = \frac{-155}{638} & & \\ & V = \left\{ \frac{-155}{638} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{9})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -6x+\frac{4}{9}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+28} & = & \color{red}{441x} +54 \\\Leftrightarrow & -378x \color{red}{+28} \color{blue}{-28} \color{blue}{-441x} & = & \color{red}{441x} +54 \color{blue}{-441x} \color{blue}{-28} \\\Leftrightarrow & -378x-441x& = & 54-28 \\\Leftrightarrow & \color{red}{-819} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-819} & & \\\Leftrightarrow & x = \frac{-2}{63} & & \\ & V = \left\{ \frac{-2}{63} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-88}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{-165} & = & \color{red}{-88x} +24 \\\Leftrightarrow & 660x \color{red}{-165} \color{blue}{+165} \color{blue}{+88x} & = & \color{red}{-88x} +24 \color{blue}{+88x} \color{blue}{+165} \\\Leftrightarrow & 660x+88x& = & 24+165 \\\Leftrightarrow & \color{red}{748} x& = & 189 \\\Leftrightarrow & x = \frac{189}{748} & & \\ & V = \left\{ \frac{189}{748} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & -9x+\frac{5}{9} \\\Leftrightarrow & 10x-\frac{15}{11}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-135} & = & \color{red}{-891x} +55 \\\Leftrightarrow & 990x \color{red}{-135} \color{blue}{+135} \color{blue}{+891x} & = & \color{red}{-891x} +55 \color{blue}{+891x} \color{blue}{+135} \\\Leftrightarrow & 990x+891x& = & 55+135 \\\Leftrightarrow & \color{red}{1881} x& = & 190 \\\Leftrightarrow & x = \frac{190}{1881} & & \\\Leftrightarrow & x = \frac{10}{99} & & \\ & V = \left\{ \frac{10}{99} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{11})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+48} & = & \color{red}{99x} +55 \\\Leftrightarrow & -660x \color{red}{+48} \color{blue}{-48} \color{blue}{-99x} & = & \color{red}{99x} +55 \color{blue}{-99x} \color{blue}{-48} \\\Leftrightarrow & -660x-99x& = & 55-48 \\\Leftrightarrow & \color{red}{-759} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-759} & & \\\Leftrightarrow & x = \frac{-7}{759} & & \\ & V = \left\{ \frac{-7}{759} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{24}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-216} & = & \color{red}{315x} +56 \\\Leftrightarrow & 756x \color{red}{-216} \color{blue}{+216} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+216} \\\Leftrightarrow & 756x-315x& = & 56+216 \\\Leftrightarrow & \color{red}{441} x& = & 272 \\\Leftrightarrow & x = \frac{272}{441} & & \\ & V = \left\{ \frac{272}{441} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & 9x+\frac{7}{10} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 9x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1440}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1440x \color{red}{+80} & = & \color{red}{810x} +63 \\\Leftrightarrow & 1440x \color{red}{+80} \color{blue}{-80} \color{blue}{-810x} & = & \color{red}{810x} +63 \color{blue}{-810x} \color{blue}{-80} \\\Leftrightarrow & 1440x-810x& = & 63-80 \\\Leftrightarrow & \color{red}{630} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{630} & & \\ & V = \left\{ \frac{-17}{630} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{28}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{28}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+28} & = & \color{red}{-15x} +6 \\\Leftrightarrow & -70x \color{red}{+28} \color{blue}{-28} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{-28} \\\Leftrightarrow & -70x+15x& = & 6-28 \\\Leftrightarrow & \color{red}{-55} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-55} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
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