Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{10}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-110} & = & \color{red}{693x} +54 \\\Leftrightarrow & 1980x \color{red}{-110} \color{blue}{+110} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{+110} \\\Leftrightarrow & 1980x-693x& = & 54+110 \\\Leftrightarrow & \color{red}{1287} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1287} & & \\ & V = \left\{ \frac{164}{1287} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{4}{3}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{12}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-12} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 72x \color{red}{-12} \color{blue}{+12} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+12} \\\Leftrightarrow & 72x+27x& = & 8+12 \\\Leftrightarrow & \color{red}{99} x& = & 20 \\\Leftrightarrow & x = \frac{20}{99} & & \\ & V = \left\{ \frac{20}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{441x} +14 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 252x-441x& = & 14-54 \\\Leftrightarrow & \color{red}{-189} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-189} & & \\\Leftrightarrow & x = \frac{40}{189} & & \\ & V = \left\{ \frac{40}{189} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x-\frac{15}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{-60} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 528x \color{red}{-60} \color{blue}{+60} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+60} \\\Leftrightarrow & 528x+220x& = & 99+60 \\\Leftrightarrow & \color{red}{748} x& = & 159 \\\Leftrightarrow & x = \frac{159}{748} & & \\ & V = \left\{ \frac{159}{748} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -100x+35x& = & 8+12 \\\Leftrightarrow & \color{red}{-65} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-65} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -240x+105x& = & 50+36 \\\Leftrightarrow & \color{red}{-135} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-135} & & \\\Leftrightarrow & x = \frac{-86}{135} & & \\ & V = \left\{ \frac{-86}{135} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{6})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{25}{6}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{990}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{-264}{ \color{blue}{66} }x+ \frac{24}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 990x \color{red}{-275} & = & \color{red}{-264x} +24 \\\Leftrightarrow & 990x \color{red}{-275} \color{blue}{+275} \color{blue}{+264x} & = & \color{red}{-264x} +24 \color{blue}{+264x} \color{blue}{+275} \\\Leftrightarrow & 990x+264x& = & 24+275 \\\Leftrightarrow & \color{red}{1254} x& = & 299 \\\Leftrightarrow & x = \frac{299}{1254} & & \\ & V = \left\{ \frac{299}{1254} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & 6x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{18}{5}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+198} & = & \color{red}{330x} +30 \\\Leftrightarrow & -990x \color{red}{+198} \color{blue}{-198} \color{blue}{-330x} & = & \color{red}{330x} +30 \color{blue}{-330x} \color{blue}{-198} \\\Leftrightarrow & -990x-330x& = & 30-198 \\\Leftrightarrow & \color{red}{-1320} x& = & -168 \\\Leftrightarrow & x = \frac{-168}{-1320} & & \\\Leftrightarrow & x = \frac{7}{55} & & \\ & V = \left\{ \frac{7}{55} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-8} & = & \color{red}{-15x} +8 \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+8} \\\Leftrightarrow & -12x+15x& = & 8+8 \\\Leftrightarrow & \color{red}{3} x& = & 16 \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+50} & = & \color{red}{280x} +42 \\\Leftrightarrow & -875x \color{red}{+50} \color{blue}{-50} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-50} \\\Leftrightarrow & -875x-280x& = & 42-50 \\\Leftrightarrow & \color{red}{-1155} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-1155} & & \\\Leftrightarrow & x = \frac{8}{1155} & & \\ & V = \left\{ \frac{8}{1155} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -30x+\frac{12}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{+108} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -1890x \color{red}{+108} \color{blue}{-108} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{-108} \\\Leftrightarrow & -1890x+441x& = & 49-108 \\\Leftrightarrow & \color{red}{-1449} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-1449} & & \\\Leftrightarrow & x = \frac{59}{1449} & & \\ & V = \left\{ \frac{59}{1449} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{6})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{25}{6}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-25} & = & \color{red}{-54x} +27 \\\Leftrightarrow & -120x \color{red}{-25} \color{blue}{+25} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+25} \\\Leftrightarrow & -120x+54x& = & 27+25 \\\Leftrightarrow & \color{red}{-66} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-66} & & \\\Leftrightarrow & x = \frac{-26}{33} & & \\ & V = \left\{ \frac{-26}{33} \right\} & \\\end{align}\)
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