Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-2)& = & 2x+\frac{3}{7} \\\Leftrightarrow & -28x+14& = & 2x+\frac{3}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-196}{ \color{blue}{7} }x+ \frac{98}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -196x \color{red}{+98} & = & \color{red}{14x} +3 \\\Leftrightarrow & -196x \color{red}{+98} \color{blue}{-98} \color{blue}{-14x} & = & \color{red}{14x} +3 \color{blue}{-14x} \color{blue}{-98} \\\Leftrightarrow & -196x-14x& = & 3-98 \\\Leftrightarrow & \color{red}{-210} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-210} & & \\\Leftrightarrow & x = \frac{19}{42} & & \\ & V = \left\{ \frac{19}{42} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-60} & = & \color{red}{-63x} +7 \\\Leftrightarrow & -180x \color{red}{-60} \color{blue}{+60} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{+60} \\\Leftrightarrow & -180x+63x& = & 7+60 \\\Leftrightarrow & \color{red}{-117} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-117} & & \\\Leftrightarrow & x = \frac{-67}{117} & & \\ & V = \left\{ \frac{-67}{117} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +35 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +35 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 35+36 \\\Leftrightarrow & \color{red}{-255} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-255} & & \\\Leftrightarrow & x = \frac{-71}{255} & & \\ & V = \left\{ \frac{-71}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{11})& = & -3x+\frac{7}{11} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+35} & = & \color{red}{-33x} +7 \\\Leftrightarrow & -154x \color{red}{+35} \color{blue}{-35} \color{blue}{+33x} & = & \color{red}{-33x} +7 \color{blue}{+33x} \color{blue}{-35} \\\Leftrightarrow & -154x+33x& = & 7-35 \\\Leftrightarrow & \color{red}{-121} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-121} & & \\\Leftrightarrow & x = \frac{28}{121} & & \\ & V = \left\{ \frac{28}{121} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -8x+\frac{8}{11} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-154} & = & \color{red}{-264x} +24 \\\Leftrightarrow & -924x \color{red}{-154} \color{blue}{+154} \color{blue}{+264x} & = & \color{red}{-264x} +24 \color{blue}{+264x} \color{blue}{+154} \\\Leftrightarrow & -924x+264x& = & 24+154 \\\Leftrightarrow & \color{red}{-660} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-660} & & \\\Leftrightarrow & x = \frac{-89}{330} & & \\ & V = \left\{ \frac{-89}{330} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & -3x+\frac{3}{8} \\\Leftrightarrow & -35x-\frac{28}{9}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x- \frac{224}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{-224} & = & \color{red}{-216x} +27 \\\Leftrightarrow & -2520x \color{red}{-224} \color{blue}{+224} \color{blue}{+216x} & = & \color{red}{-216x} +27 \color{blue}{+216x} \color{blue}{+224} \\\Leftrightarrow & -2520x+216x& = & 27+224 \\\Leftrightarrow & \color{red}{-2304} x& = & 251 \\\Leftrightarrow & x = \frac{251}{-2304} & & \\\Leftrightarrow & x = \frac{-251}{2304} & & \\ & V = \left\{ \frac{-251}{2304} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 16x-\frac{16}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{-48} & = & \color{red}{-99x} +88 \\\Leftrightarrow & 528x \color{red}{-48} \color{blue}{+48} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{+48} \\\Leftrightarrow & 528x+99x& = & 88+48 \\\Leftrightarrow & \color{red}{627} x& = & 136 \\\Leftrightarrow & x = \frac{136}{627} & & \\ & V = \left\{ \frac{136}{627} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{2})& = & -7x+\frac{7}{11} \\\Leftrightarrow & 20x+\frac{25}{2}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+275} & = & \color{red}{-154x} +14 \\\Leftrightarrow & 440x \color{red}{+275} \color{blue}{-275} \color{blue}{+154x} & = & \color{red}{-154x} +14 \color{blue}{+154x} \color{blue}{-275} \\\Leftrightarrow & 440x+154x& = & 14-275 \\\Leftrightarrow & \color{red}{594} x& = & -261 \\\Leftrightarrow & x = \frac{-261}{594} & & \\\Leftrightarrow & x = \frac{-29}{66} & & \\ & V = \left\{ \frac{-29}{66} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+84} & = & \color{red}{385x} +66 \\\Leftrightarrow & -924x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & -924x-385x& = & 66-84 \\\Leftrightarrow & \color{red}{-1309} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-1309} & & \\\Leftrightarrow & x = \frac{18}{1309} & & \\ & V = \left\{ \frac{18}{1309} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{12}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+24} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 396x \color{red}{+24} \color{blue}{-24} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-24} \\\Leftrightarrow & 396x+154x& = & 33-24 \\\Leftrightarrow & \color{red}{550} x& = & 9 \\\Leftrightarrow & x = \frac{9}{550} & & \\ & V = \left\{ \frac{9}{550} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{9})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{20}{9}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-140} & = & \color{red}{-315x} +27 \\\Leftrightarrow & 756x \color{red}{-140} \color{blue}{+140} \color{blue}{+315x} & = & \color{red}{-315x} +27 \color{blue}{+315x} \color{blue}{+140} \\\Leftrightarrow & 756x+315x& = & 27+140 \\\Leftrightarrow & \color{red}{1071} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1071} & & \\ & V = \left\{ \frac{167}{1071} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{4})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{21}{4}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{392}{ \color{blue}{28} }x+ \frac{147}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 392x \color{red}{+147} & = & \color{red}{-140x} +16 \\\Leftrightarrow & 392x \color{red}{+147} \color{blue}{-147} \color{blue}{+140x} & = & \color{red}{-140x} +16 \color{blue}{+140x} \color{blue}{-147} \\\Leftrightarrow & 392x+140x& = & 16-147 \\\Leftrightarrow & \color{red}{532} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{532} & & \\ & V = \left\{ \frac{-131}{532} \right\} & \\\end{align}\)
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