Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -14x+\frac{28}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x+ \frac{56}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{+56} & = & \color{red}{66x} +55 \\\Leftrightarrow & -308x \color{red}{+56} \color{blue}{-56} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{-56} \\\Leftrightarrow & -308x-66x& = & 55-56 \\\Leftrightarrow & \color{red}{-374} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-374} & & \\\Leftrightarrow & x = \frac{1}{374} & & \\ & V = \left\{ \frac{1}{374} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-168} & = & \color{red}{175x} +10 \\\Leftrightarrow & 630x \color{red}{-168} \color{blue}{+168} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{+168} \\\Leftrightarrow & 630x-175x& = & 10+168 \\\Leftrightarrow & \color{red}{455} x& = & 178 \\\Leftrightarrow & x = \frac{178}{455} & & \\ & V = \left\{ \frac{178}{455} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-24} & = & \color{red}{55x} +6 \\\Leftrightarrow & -132x \color{red}{-24} \color{blue}{+24} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+24} \\\Leftrightarrow & -132x-55x& = & 6+24 \\\Leftrightarrow & \color{red}{-187} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-187} & & \\\Leftrightarrow & x = \frac{-30}{187} & & \\ & V = \left\{ \frac{-30}{187} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-6} & = & \color{red}{35x} +7 \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +7 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -30x-35x& = & 7+6 \\\Leftrightarrow & \color{red}{-65} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-65} & & \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{308x} +99 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+40} \\\Leftrightarrow & -440x-308x& = & 99+40 \\\Leftrightarrow & \color{red}{-748} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-748} & & \\\Leftrightarrow & x = \frac{-139}{748} & & \\ & V = \left\{ \frac{-139}{748} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 4x+\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{441x} +36 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & 252x-441x& = & 36-56 \\\Leftrightarrow & \color{red}{-189} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-189} & & \\\Leftrightarrow & x = \frac{20}{189} & & \\ & V = \left\{ \frac{20}{189} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+20} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & -30x+21x& = & 10-20 \\\Leftrightarrow & \color{red}{-9} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-9} & & \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{11})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{12}{11}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+12} & = & \color{red}{-44x} +10 \\\Leftrightarrow & -165x \color{red}{+12} \color{blue}{-12} \color{blue}{+44x} & = & \color{red}{-44x} +10 \color{blue}{+44x} \color{blue}{-12} \\\Leftrightarrow & -165x+44x& = & 10-12 \\\Leftrightarrow & \color{red}{-121} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-121} & & \\\Leftrightarrow & x = \frac{2}{121} & & \\ & V = \left\{ \frac{2}{121} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-168} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 924x \color{red}{-168} \color{blue}{+168} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{+168} \\\Leftrightarrow & 924x+539x& = & 66+168 \\\Leftrightarrow & \color{red}{1463} x& = & 234 \\\Leftrightarrow & x = \frac{234}{1463} & & \\ & V = \left\{ \frac{234}{1463} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{16}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+48} & = & \color{red}{231x} +110 \\\Leftrightarrow & 660x \color{red}{+48} \color{blue}{-48} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-48} \\\Leftrightarrow & 660x-231x& = & 110-48 \\\Leftrightarrow & \color{red}{429} x& = & 62 \\\Leftrightarrow & x = \frac{62}{429} & & \\ & V = \left\{ \frac{62}{429} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{+16} & = & \color{red}{-90x} +27 \\\Leftrightarrow & -72x \color{red}{+16} \color{blue}{-16} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{-16} \\\Leftrightarrow & -72x+90x& = & 27-16 \\\Leftrightarrow & \color{red}{18} x& = & 11 \\\Leftrightarrow & x = \frac{11}{18} & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{8})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 9x+\frac{9}{8}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{+45} & = & \color{red}{280x} +16 \\\Leftrightarrow & 360x \color{red}{+45} \color{blue}{-45} \color{blue}{-280x} & = & \color{red}{280x} +16 \color{blue}{-280x} \color{blue}{-45} \\\Leftrightarrow & 360x-280x& = & 16-45 \\\Leftrightarrow & \color{red}{80} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{80} & & \\ & V = \left\{ \frac{-29}{80} \right\} & \\\end{align}\)
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