Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 4x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-6} & = & \color{red}{20x} +8 \\\Leftrightarrow & -75x \color{red}{-6} \color{blue}{+6} \color{blue}{-20x} & = & \color{red}{20x} +8 \color{blue}{-20x} \color{blue}{+6} \\\Leftrightarrow & -75x-20x& = & 8+6 \\\Leftrightarrow & \color{red}{-95} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-95} & & \\\Leftrightarrow & x = \frac{-14}{95} & & \\ & V = \left\{ \frac{-14}{95} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2112}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2112x \color{red}{-144} & = & \color{red}{-440x} +77 \\\Leftrightarrow & -2112x \color{red}{-144} \color{blue}{+144} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{+144} \\\Leftrightarrow & -2112x+440x& = & 77+144 \\\Leftrightarrow & \color{red}{-1672} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1672} & & \\\Leftrightarrow & x = \frac{-221}{1672} & & \\ & V = \left\{ \frac{-221}{1672} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 4x+\frac{10}{3}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{12}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 12x \color{red}{+10} & = & \color{red}{15x} +8 \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-15x} & = & \color{red}{15x} +8 \color{blue}{-15x} \color{blue}{-10} \\\Leftrightarrow & 12x-15x& = & 8-10 \\\Leftrightarrow & \color{red}{-3} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-3} & & \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{5}{3} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{165x} +55 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +55 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -792x-165x& = & 55+54 \\\Leftrightarrow & \color{red}{-957} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-957} & & \\\Leftrightarrow & x = \frac{-109}{957} & & \\ & V = \left\{ \frac{-109}{957} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{8}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-88} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{-88} \color{blue}{+88} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+88} \\\Leftrightarrow & 924x-385x& = & 42+88 \\\Leftrightarrow & \color{red}{539} x& = & 130 \\\Leftrightarrow & x = \frac{130}{539} & & \\ & V = \left\{ \frac{130}{539} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 6x+\frac{7}{12} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 6x+\frac{7}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{14}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{144x} +14 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{-144x} & = & \color{red}{144x} +14 \color{blue}{-144x} \color{blue}{+63} \\\Leftrightarrow & -840x-144x& = & 14+63 \\\Leftrightarrow & \color{red}{-984} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-984} & & \\\Leftrightarrow & x = \frac{-77}{984} & & \\ & V = \left\{ \frac{-77}{984} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{11})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+50} & = & \color{red}{165x} +44 \\\Leftrightarrow & 550x \color{red}{+50} \color{blue}{-50} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-50} \\\Leftrightarrow & 550x-165x& = & 44-50 \\\Leftrightarrow & \color{red}{385} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{385} & & \\ & V = \left\{ \frac{-6}{385} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+150} & = & \color{red}{275x} +88 \\\Leftrightarrow & -990x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & -990x-275x& = & 88-150 \\\Leftrightarrow & \color{red}{-1265} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-1265} & & \\\Leftrightarrow & x = \frac{62}{1265} & & \\ & V = \left\{ \frac{62}{1265} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{-135x} +50 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & 120x+135x& = & 50+36 \\\Leftrightarrow & \color{red}{255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{255} & & \\ & V = \left\{ \frac{86}{255} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -396x-165x& = & 22+54 \\\Leftrightarrow & \color{red}{-561} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-561} & & \\\Leftrightarrow & x = \frac{-76}{561} & & \\ & V = \left\{ \frac{-76}{561} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 6x-\frac{8}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-40} & = & \color{red}{245x} +14 \\\Leftrightarrow & 210x \color{red}{-40} \color{blue}{+40} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{+40} \\\Leftrightarrow & 210x-245x& = & 14+40 \\\Leftrightarrow & \color{red}{-35} x& = & 54 \\\Leftrightarrow & x = \frac{54}{-35} & & \\\Leftrightarrow & x = \frac{-54}{35} & & \\ & V = \left\{ \frac{-54}{35} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x-\frac{4}{3}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{44}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-44} & = & \color{red}{231x} +24 \\\Leftrightarrow & -330x \color{red}{-44} \color{blue}{+44} \color{blue}{-231x} & = & \color{red}{231x} +24 \color{blue}{-231x} \color{blue}{+44} \\\Leftrightarrow & -330x-231x& = & 24+44 \\\Leftrightarrow & \color{red}{-561} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-561} & & \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
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