Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x+\frac{15}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x+ \frac{60}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-140x} +21 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{-60} \\\Leftrightarrow & -252x+140x& = & 21-60 \\\Leftrightarrow & \color{red}{-112} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-112} & & \\\Leftrightarrow & x = \frac{39}{112} & & \\ & V = \left\{ \frac{39}{112} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{8}{9}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{-88} & = & \color{red}{495x} +54 \\\Leftrightarrow & -396x \color{red}{-88} \color{blue}{+88} \color{blue}{-495x} & = & \color{red}{495x} +54 \color{blue}{-495x} \color{blue}{+88} \\\Leftrightarrow & -396x-495x& = & 54+88 \\\Leftrightarrow & \color{red}{-891} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-891} & & \\\Leftrightarrow & x = \frac{-142}{891} & & \\ & V = \left\{ \frac{-142}{891} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{147x} +28 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+90} \\\Leftrightarrow & -630x-147x& = & 28+90 \\\Leftrightarrow & \color{red}{-777} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-777} & & \\\Leftrightarrow & x = \frac{-118}{777} & & \\ & V = \left\{ \frac{-118}{777} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{7})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -6x+\frac{9}{7}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-252}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -252x \color{red}{+54} & = & \color{red}{294x} +49 \\\Leftrightarrow & -252x \color{red}{+54} \color{blue}{-54} \color{blue}{-294x} & = & \color{red}{294x} +49 \color{blue}{-294x} \color{blue}{-54} \\\Leftrightarrow & -252x-294x& = & 49-54 \\\Leftrightarrow & \color{red}{-546} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-546} & & \\\Leftrightarrow & x = \frac{5}{546} & & \\ & V = \left\{ \frac{5}{546} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 9x+\frac{5}{12} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1512}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1512x \color{red}{-360} & = & \color{red}{756x} +35 \\\Leftrightarrow & -1512x \color{red}{-360} \color{blue}{+360} \color{blue}{-756x} & = & \color{red}{756x} +35 \color{blue}{-756x} \color{blue}{+360} \\\Leftrightarrow & -1512x-756x& = & 35+360 \\\Leftrightarrow & \color{red}{-2268} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-2268} & & \\\Leftrightarrow & x = \frac{-395}{2268} & & \\ & V = \left\{ \frac{-395}{2268} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{7})& = & 2x+\frac{9}{4} \\\Leftrightarrow & -25x+\frac{25}{7}& = & 2x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x+ \frac{100}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{+100} & = & \color{red}{56x} +63 \\\Leftrightarrow & -700x \color{red}{+100} \color{blue}{-100} \color{blue}{-56x} & = & \color{red}{56x} +63 \color{blue}{-56x} \color{blue}{-100} \\\Leftrightarrow & -700x-56x& = & 63-100 \\\Leftrightarrow & \color{red}{-756} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-756} & & \\\Leftrightarrow & x = \frac{37}{756} & & \\ & V = \left\{ \frac{37}{756} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{9})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x+\frac{25}{9}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+50} & = & \color{red}{126x} +63 \\\Leftrightarrow & -180x \color{red}{+50} \color{blue}{-50} \color{blue}{-126x} & = & \color{red}{126x} +63 \color{blue}{-126x} \color{blue}{-50} \\\Leftrightarrow & -180x-126x& = & 63-50 \\\Leftrightarrow & \color{red}{-306} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-306} & & \\\Leftrightarrow & x = \frac{-13}{306} & & \\ & V = \left\{ \frac{-13}{306} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+60} & = & \color{red}{-63x} +14 \\\Leftrightarrow & -420x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & -420x+63x& = & 14-60 \\\Leftrightarrow & \color{red}{-357} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-357} & & \\\Leftrightarrow & x = \frac{46}{357} & & \\ & V = \left\{ \frac{46}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{12})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{25}{12}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-25} & = & \color{red}{-84x} +27 \\\Leftrightarrow & 240x \color{red}{-25} \color{blue}{+25} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{+25} \\\Leftrightarrow & 240x+84x& = & 27+25 \\\Leftrightarrow & \color{red}{324} x& = & 52 \\\Leftrightarrow & x = \frac{52}{324} & & \\\Leftrightarrow & x = \frac{13}{81} & & \\ & V = \left\{ \frac{13}{81} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{385x} +45 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +45 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1650x-385x& = & 45-132 \\\Leftrightarrow & \color{red}{1265} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{1265} & & \\ & V = \left\{ \frac{-87}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+176} & = & \color{red}{-693x} +70 \\\Leftrightarrow & 1540x \color{red}{+176} \color{blue}{-176} \color{blue}{+693x} & = & \color{red}{-693x} +70 \color{blue}{+693x} \color{blue}{-176} \\\Leftrightarrow & 1540x+693x& = & 70-176 \\\Leftrightarrow & \color{red}{2233} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{2233} & & \\ & V = \left\{ \frac{-106}{2233} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & -6x+\frac{7}{2} \\\Leftrightarrow & -18x+\frac{18}{11}& = & -6x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-132}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{-132x} +77 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{+132x} & = & \color{red}{-132x} +77 \color{blue}{+132x} \color{blue}{-36} \\\Leftrightarrow & -396x+132x& = & 77-36 \\\Leftrightarrow & \color{red}{-264} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-264} & & \\\Leftrightarrow & x = \frac{-41}{264} & & \\ & V = \left\{ \frac{-41}{264} \right\} & \\\end{align}\)
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