Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+330} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -1848x+385x& = & 42-330 \\\Leftrightarrow & \color{red}{-1463} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{-1463} & & \\\Leftrightarrow & x = \frac{288}{1463} & & \\ & V = \left\{ \frac{288}{1463} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{9}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+27} & = & \color{red}{105x} +14 \\\Leftrightarrow & -252x \color{red}{+27} \color{blue}{-27} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-27} \\\Leftrightarrow & -252x-105x& = & 14-27 \\\Leftrightarrow & \color{red}{-357} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-357} & & \\\Leftrightarrow & x = \frac{13}{357} & & \\ & V = \left\{ \frac{13}{357} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+20} & = & \color{red}{70x} +35 \\\Leftrightarrow & -56x \color{red}{+20} \color{blue}{-20} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{-20} \\\Leftrightarrow & -56x-70x& = & 35-20 \\\Leftrightarrow & \color{red}{-126} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-126} & & \\\Leftrightarrow & x = \frac{-5}{42} & & \\ & V = \left\{ \frac{-5}{42} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{2})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -35x+\frac{35}{2}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-490}{ \color{blue}{14} }x+ \frac{245}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -490x \color{red}{+245} & = & \color{red}{42x} +20 \\\Leftrightarrow & -490x \color{red}{+245} \color{blue}{-245} \color{blue}{-42x} & = & \color{red}{42x} +20 \color{blue}{-42x} \color{blue}{-245} \\\Leftrightarrow & -490x-42x& = & 20-245 \\\Leftrightarrow & \color{red}{-532} x& = & -225 \\\Leftrightarrow & x = \frac{-225}{-532} & & \\\Leftrightarrow & x = \frac{225}{532} & & \\ & V = \left\{ \frac{225}{532} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{-15} & = & \color{red}{20x} +18 \\\Leftrightarrow & -36x \color{red}{-15} \color{blue}{+15} \color{blue}{-20x} & = & \color{red}{20x} +18 \color{blue}{-20x} \color{blue}{+15} \\\Leftrightarrow & -36x-20x& = & 18+15 \\\Leftrightarrow & \color{red}{-56} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-56} & & \\\Leftrightarrow & x = \frac{-33}{56} & & \\ & V = \left\{ \frac{-33}{56} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -135x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-210} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-210} & & \\\Leftrightarrow & x = \frac{13}{105} & & \\ & V = \left\{ \frac{13}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & -3x+\frac{9}{8} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1400}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1400x \color{red}{-80} & = & \color{red}{-168x} +63 \\\Leftrightarrow & -1400x \color{red}{-80} \color{blue}{+80} \color{blue}{+168x} & = & \color{red}{-168x} +63 \color{blue}{+168x} \color{blue}{+80} \\\Leftrightarrow & -1400x+168x& = & 63+80 \\\Leftrightarrow & \color{red}{-1232} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1232} & & \\\Leftrightarrow & x = \frac{-13}{112} & & \\ & V = \left\{ \frac{-13}{112} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{8})& = & 2x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{-165} & = & \color{red}{176x} +80 \\\Leftrightarrow & 1320x \color{red}{-165} \color{blue}{+165} \color{blue}{-176x} & = & \color{red}{176x} +80 \color{blue}{-176x} \color{blue}{+165} \\\Leftrightarrow & 1320x-176x& = & 80+165 \\\Leftrightarrow & \color{red}{1144} x& = & 245 \\\Leftrightarrow & x = \frac{245}{1144} & & \\ & V = \left\{ \frac{245}{1144} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{4})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 9x-\frac{9}{4}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{36}{ \color{blue}{4} }x- \frac{9}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 36x \color{red}{-9} & = & \color{red}{32x} +18 \\\Leftrightarrow & 36x \color{red}{-9} \color{blue}{+9} \color{blue}{-32x} & = & \color{red}{32x} +18 \color{blue}{-32x} \color{blue}{+9} \\\Leftrightarrow & 36x-32x& = & 18+9 \\\Leftrightarrow & \color{red}{4} x& = & 27 \\\Leftrightarrow & x = \frac{27}{4} & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-330} & = & \color{red}{-693x} +42 \\\Leftrightarrow & -1386x \color{red}{-330} \color{blue}{+330} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{+330} \\\Leftrightarrow & -1386x+693x& = & 42+330 \\\Leftrightarrow & \color{red}{-693} x& = & 372 \\\Leftrightarrow & x = \frac{372}{-693} & & \\\Leftrightarrow & x = \frac{-124}{231} & & \\ & V = \left\{ \frac{-124}{231} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{15x} +5 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +5 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & 36x-15x& = & 5-8 \\\Leftrightarrow & \color{red}{21} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{21} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -24x+\frac{30}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+30} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -264x \color{red}{+30} \color{blue}{-30} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-30} \\\Leftrightarrow & -264x+55x& = & 6-30 \\\Leftrightarrow & \color{red}{-209} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-209} & & \\\Leftrightarrow & x = \frac{24}{209} & & \\ & V = \left\{ \frac{24}{209} \right\} & \\\end{align}\)
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