Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-105} & = & \color{red}{-280x} +80 \\\Leftrightarrow & -672x \color{red}{-105} \color{blue}{+105} \color{blue}{+280x} & = & \color{red}{-280x} +80 \color{blue}{+280x} \color{blue}{+105} \\\Leftrightarrow & -672x+280x& = & 80+105 \\\Leftrightarrow & \color{red}{-392} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-392} & & \\\Leftrightarrow & x = \frac{-185}{392} & & \\ & V = \left\{ \frac{-185}{392} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{10}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{+10} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -18x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & -18x+21x& = & 10-10 \\\Leftrightarrow & \color{red}{3} x& = & 0 \\\Leftrightarrow & x = \frac{0}{3} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{+270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 1512x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & 1512x+315x& = & 56-270 \\\Leftrightarrow & \color{red}{1827} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{1827} & & \\ & V = \left\{ \frac{-214}{1827} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-220} & = & \color{red}{231x} +18 \\\Leftrightarrow & -330x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & -330x-231x& = & 18+220 \\\Leftrightarrow & \color{red}{-561} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-561} & & \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -20x+\frac{15}{8}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1440}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1440x \color{red}{+135} & = & \color{red}{216x} +80 \\\Leftrightarrow & -1440x \color{red}{+135} \color{blue}{-135} \color{blue}{-216x} & = & \color{red}{216x} +80 \color{blue}{-216x} \color{blue}{-135} \\\Leftrightarrow & -1440x-216x& = & 80-135 \\\Leftrightarrow & \color{red}{-1656} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-1656} & & \\\Leftrightarrow & x = \frac{55}{1656} & & \\ & V = \left\{ \frac{55}{1656} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & -4x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -4x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-220} & = & \color{red}{-396x} +45 \\\Leftrightarrow & -1485x \color{red}{-220} \color{blue}{+220} \color{blue}{+396x} & = & \color{red}{-396x} +45 \color{blue}{+396x} \color{blue}{+220} \\\Leftrightarrow & -1485x+396x& = & 45+220 \\\Leftrightarrow & \color{red}{-1089} x& = & 265 \\\Leftrightarrow & x = \frac{265}{-1089} & & \\\Leftrightarrow & x = \frac{-265}{1089} & & \\ & V = \left\{ \frac{-265}{1089} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{3})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 4x-\frac{4}{3}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-28} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 84x \color{red}{-28} \color{blue}{+28} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+28} \\\Leftrightarrow & 84x+105x& = & 18+28 \\\Leftrightarrow & \color{red}{189} x& = & 46 \\\Leftrightarrow & x = \frac{46}{189} & & \\ & V = \left\{ \frac{46}{189} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 18x+\frac{18}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{90}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{-90} \\\Leftrightarrow & 630x+175x& = & 56-90 \\\Leftrightarrow & \color{red}{805} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{805} & & \\ & V = \left\{ \frac{-34}{805} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{7})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 30x+\frac{24}{7}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+264} & = & \color{red}{-539x} +63 \\\Leftrightarrow & 2310x \color{red}{+264} \color{blue}{-264} \color{blue}{+539x} & = & \color{red}{-539x} +63 \color{blue}{+539x} \color{blue}{-264} \\\Leftrightarrow & 2310x+539x& = & 63-264 \\\Leftrightarrow & \color{red}{2849} x& = & -201 \\\Leftrightarrow & x = \frac{-201}{2849} & & \\ & V = \left\{ \frac{-201}{2849} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & 9x+\frac{9}{5} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-50} & = & \color{red}{495x} +99 \\\Leftrightarrow & 440x \color{red}{-50} \color{blue}{+50} \color{blue}{-495x} & = & \color{red}{495x} +99 \color{blue}{-495x} \color{blue}{+50} \\\Leftrightarrow & 440x-495x& = & 99+50 \\\Leftrightarrow & \color{red}{-55} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-55} & & \\\Leftrightarrow & x = \frac{-149}{55} & & \\ & V = \left\{ \frac{-149}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x+ \frac{32}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{+32} & = & \color{red}{154x} +33 \\\Leftrightarrow & 352x \color{red}{+32} \color{blue}{-32} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-32} \\\Leftrightarrow & 352x-154x& = & 33-32 \\\Leftrightarrow & \color{red}{198} x& = & 1 \\\Leftrightarrow & x = \frac{1}{198} & & \\ & V = \left\{ \frac{1}{198} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{7})& = & 8x+\frac{7}{12} \\\Leftrightarrow & -21x-4& = & 8x+\frac{7}{12} \\ & & & \text{kgv van noemers 1 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{48}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-48} & = & \color{red}{96x} +7 \\\Leftrightarrow & -252x \color{red}{-48} \color{blue}{+48} \color{blue}{-96x} & = & \color{red}{96x} +7 \color{blue}{-96x} \color{blue}{+48} \\\Leftrightarrow & -252x-96x& = & 7+48 \\\Leftrightarrow & \color{red}{-348} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-348} & & \\\Leftrightarrow & x = \frac{-55}{348} & & \\ & V = \left\{ \frac{-55}{348} \right\} & \\\end{align}\)
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