Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-180} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -630x \color{red}{-180} \color{blue}{+180} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{+180} \\\Leftrightarrow & -630x+441x& = & 49+180 \\\Leftrightarrow & \color{red}{-189} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-189} & & \\\Leftrightarrow & x = \frac{-229}{189} & & \\ & V = \left\{ \frac{-229}{189} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{+84} & = & \color{red}{315x} +40 \\\Leftrightarrow & 560x \color{red}{+84} \color{blue}{-84} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-84} \\\Leftrightarrow & 560x-315x& = & 40-84 \\\Leftrightarrow & \color{red}{245} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{245} & & \\ & V = \left\{ \frac{-44}{245} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+70} & = & \color{red}{-120x} +18 \\\Leftrightarrow & -315x \color{red}{+70} \color{blue}{-70} \color{blue}{+120x} & = & \color{red}{-120x} +18 \color{blue}{+120x} \color{blue}{-70} \\\Leftrightarrow & -315x+120x& = & 18-70 \\\Leftrightarrow & \color{red}{-195} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-195} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 4x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{132x} +18 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-132x} & = & \color{red}{132x} +18 \color{blue}{-132x} \color{blue}{+154} \\\Leftrightarrow & 693x-132x& = & 18+154 \\\Leftrightarrow & \color{red}{561} x& = & 172 \\\Leftrightarrow & x = \frac{172}{561} & & \\ & V = \left\{ \frac{172}{561} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{49x} +6 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+30} \\\Leftrightarrow & -210x-49x& = & 6+30 \\\Leftrightarrow & \color{red}{-259} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-259} & & \\\Leftrightarrow & x = \frac{-36}{259} & & \\ & V = \left\{ \frac{-36}{259} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x+\frac{6}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+42} & = & \color{red}{539x} +44 \\\Leftrightarrow & -770x \color{red}{+42} \color{blue}{-42} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{-42} \\\Leftrightarrow & -770x-539x& = & 44-42 \\\Leftrightarrow & \color{red}{-1309} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-1309} & & \\\Leftrightarrow & x = \frac{-2}{1309} & & \\ & V = \left\{ \frac{-2}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-30} & = & \color{red}{189x} +56 \\\Leftrightarrow & 168x \color{red}{-30} \color{blue}{+30} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{+30} \\\Leftrightarrow & 168x-189x& = & 56+30 \\\Leftrightarrow & \color{red}{-21} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-21} & & \\\Leftrightarrow & x = \frac{-86}{21} & & \\ & V = \left\{ \frac{-86}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -20x-\frac{16}{3}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x- \frac{128}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{-128} & = & \color{red}{168x} +9 \\\Leftrightarrow & -480x \color{red}{-128} \color{blue}{+128} \color{blue}{-168x} & = & \color{red}{168x} +9 \color{blue}{-168x} \color{blue}{+128} \\\Leftrightarrow & -480x-168x& = & 9+128 \\\Leftrightarrow & \color{red}{-648} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-648} & & \\\Leftrightarrow & x = \frac{-137}{648} & & \\ & V = \left\{ \frac{-137}{648} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-210} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 1386x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 1386x+385x& = & 110+210 \\\Leftrightarrow & \color{red}{1771} x& = & 320 \\\Leftrightarrow & x = \frac{320}{1771} & & \\ & V = \left\{ \frac{320}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2100}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2100x \color{red}{+300} & = & \color{red}{490x} +21 \\\Leftrightarrow & -2100x \color{red}{+300} \color{blue}{-300} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{-300} \\\Leftrightarrow & -2100x-490x& = & 21-300 \\\Leftrightarrow & \color{red}{-2590} x& = & -279 \\\Leftrightarrow & x = \frac{-279}{-2590} & & \\\Leftrightarrow & x = \frac{279}{2590} & & \\ & V = \left\{ \frac{279}{2590} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -10x-\frac{4}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-8} & = & \color{red}{70x} +45 \\\Leftrightarrow & -100x \color{red}{-8} \color{blue}{+8} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+8} \\\Leftrightarrow & -100x-70x& = & 45+8 \\\Leftrightarrow & \color{red}{-170} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-170} & & \\\Leftrightarrow & x = \frac{-53}{170} & & \\ & V = \left\{ \frac{-53}{170} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{15}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+45} & = & \color{red}{165x} +44 \\\Leftrightarrow & -396x \color{red}{+45} \color{blue}{-45} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-45} \\\Leftrightarrow & -396x-165x& = & 44-45 \\\Leftrightarrow & \color{red}{-561} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-561} & & \\\Leftrightarrow & x = \frac{1}{561} & & \\ & V = \left\{ \frac{1}{561} \right\} & \\\end{align}\)
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