Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{320}{ \color{blue}{40} }x- \frac{32}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 320x \color{red}{-32} & = & \color{red}{200x} +25 \\\Leftrightarrow & 320x \color{red}{-32} \color{blue}{+32} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{+32} \\\Leftrightarrow & 320x-200x& = & 25+32 \\\Leftrightarrow & \color{red}{120} x& = & 57 \\\Leftrightarrow & x = \frac{57}{120} & & \\\Leftrightarrow & x = \frac{19}{40} & & \\ & V = \left\{ \frac{19}{40} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & 4x+\frac{3}{8} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 4x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{+15} & = & \color{red}{32x} +3 \\\Leftrightarrow & -120x \color{red}{+15} \color{blue}{-15} \color{blue}{-32x} & = & \color{red}{32x} +3 \color{blue}{-32x} \color{blue}{-15} \\\Leftrightarrow & -120x-32x& = & 3-15 \\\Leftrightarrow & \color{red}{-152} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-152} & & \\\Leftrightarrow & x = \frac{3}{38} & & \\ & V = \left\{ \frac{3}{38} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 693x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & 693x+539x& = & 42-66 \\\Leftrightarrow & \color{red}{1232} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{1232} & & \\\Leftrightarrow & x = \frac{-3}{154} & & \\ & V = \left\{ \frac{-3}{154} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+10} & = & \color{red}{49x} +3 \\\Leftrightarrow & -42x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & -42x-49x& = & 3-10 \\\Leftrightarrow & \color{red}{-91} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-91} & & \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{30}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{-60} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -528x \color{red}{-60} \color{blue}{+60} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+60} \\\Leftrightarrow & -528x+154x& = & 99+60 \\\Leftrightarrow & \color{red}{-374} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-374} & & \\\Leftrightarrow & x = \frac{-159}{374} & & \\ & V = \left\{ \frac{-159}{374} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{840}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 840x \color{red}{-120} & = & \color{red}{196x} +21 \\\Leftrightarrow & 840x \color{red}{-120} \color{blue}{+120} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{+120} \\\Leftrightarrow & 840x-196x& = & 21+120 \\\Leftrightarrow & \color{red}{644} x& = & 141 \\\Leftrightarrow & x = \frac{141}{644} & & \\ & V = \left\{ \frac{141}{644} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{8}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+8} & = & \color{red}{55x} +5 \\\Leftrightarrow & -132x \color{red}{+8} \color{blue}{-8} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-8} \\\Leftrightarrow & -132x-55x& = & 5-8 \\\Leftrightarrow & \color{red}{-187} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-187} & & \\\Leftrightarrow & x = \frac{3}{187} & & \\ & V = \left\{ \frac{3}{187} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -25x-\frac{20}{9}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-900}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -900x \color{red}{-80} & = & \color{red}{-324x} +27 \\\Leftrightarrow & -900x \color{red}{-80} \color{blue}{+80} \color{blue}{+324x} & = & \color{red}{-324x} +27 \color{blue}{+324x} \color{blue}{+80} \\\Leftrightarrow & -900x+324x& = & 27+80 \\\Leftrightarrow & \color{red}{-576} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-576} & & \\\Leftrightarrow & x = \frac{-107}{576} & & \\ & V = \left\{ \frac{-107}{576} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{+48} \\\Leftrightarrow & -180x+70x& = & 25+48 \\\Leftrightarrow & \color{red}{-110} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-110} & & \\\Leftrightarrow & x = \frac{-73}{110} & & \\ & V = \left\{ \frac{-73}{110} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-192}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -192x \color{red}{+32} & = & \color{red}{84x} +5 \\\Leftrightarrow & -192x \color{red}{+32} \color{blue}{-32} \color{blue}{-84x} & = & \color{red}{84x} +5 \color{blue}{-84x} \color{blue}{-32} \\\Leftrightarrow & -192x-84x& = & 5-32 \\\Leftrightarrow & \color{red}{-276} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-276} & & \\\Leftrightarrow & x = \frac{9}{92} & & \\ & V = \left\{ \frac{9}{92} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{70x} +45 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 300x-70x& = & 45+24 \\\Leftrightarrow & \color{red}{230} x& = & 69 \\\Leftrightarrow & x = \frac{69}{230} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{3})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 10x+\frac{10}{3}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+80} & = & \color{red}{168x} +9 \\\Leftrightarrow & 240x \color{red}{+80} \color{blue}{-80} \color{blue}{-168x} & = & \color{red}{168x} +9 \color{blue}{-168x} \color{blue}{-80} \\\Leftrightarrow & 240x-168x& = & 9-80 \\\Leftrightarrow & \color{red}{72} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{72} & & \\ & V = \left\{ \frac{-71}{72} \right\} & \\\end{align}\)
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