Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{4})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 9x+\frac{9}{4}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{+81} & = & \color{red}{252x} +40 \\\Leftrightarrow & 324x \color{red}{+81} \color{blue}{-81} \color{blue}{-252x} & = & \color{red}{252x} +40 \color{blue}{-252x} \color{blue}{-81} \\\Leftrightarrow & 324x-252x& = & 40-81 \\\Leftrightarrow & \color{red}{72} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{72} & & \\ & V = \left\{ \frac{-41}{72} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -240x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{-135} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-135} & & \\\Leftrightarrow & x = \frac{-56}{135} & & \\ & V = \left\{ \frac{-56}{135} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 2x+\frac{5}{12} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 2x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+80} & = & \color{red}{24x} +5 \\\Leftrightarrow & 180x \color{red}{+80} \color{blue}{-80} \color{blue}{-24x} & = & \color{red}{24x} +5 \color{blue}{-24x} \color{blue}{-80} \\\Leftrightarrow & 180x-24x& = & 5-80 \\\Leftrightarrow & \color{red}{156} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{156} & & \\\Leftrightarrow & x = \frac{-25}{52} & & \\ & V = \left\{ \frac{-25}{52} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-44} & = & \color{red}{-385x} +45 \\\Leftrightarrow & 440x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +45 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & 440x+385x& = & 45+44 \\\Leftrightarrow & \color{red}{825} x& = & 89 \\\Leftrightarrow & x = \frac{89}{825} & & \\ & V = \left\{ \frac{89}{825} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{20}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+80} & = & \color{red}{196x} +63 \\\Leftrightarrow & 224x \color{red}{+80} \color{blue}{-80} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{-80} \\\Leftrightarrow & 224x-196x& = & 63-80 \\\Leftrightarrow & \color{red}{28} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{28} & & \\ & V = \left\{ \frac{-17}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -12x+\frac{16}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+176} & = & \color{red}{-385x} +56 \\\Leftrightarrow & -924x \color{red}{+176} \color{blue}{-176} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-176} \\\Leftrightarrow & -924x+385x& = & 56-176 \\\Leftrightarrow & \color{red}{-539} x& = & -120 \\\Leftrightarrow & x = \frac{-120}{-539} & & \\\Leftrightarrow & x = \frac{120}{539} & & \\ & V = \left\{ \frac{120}{539} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-55x} +8 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +8 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & -264x+55x& = & 8-18 \\\Leftrightarrow & \color{red}{-209} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-209} & & \\\Leftrightarrow & x = \frac{10}{209} & & \\ & V = \left\{ \frac{10}{209} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{9})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{25}{9}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-175} & = & \color{red}{-189x} +36 \\\Leftrightarrow & -1260x \color{red}{-175} \color{blue}{+175} \color{blue}{+189x} & = & \color{red}{-189x} +36 \color{blue}{+189x} \color{blue}{+175} \\\Leftrightarrow & -1260x+189x& = & 36+175 \\\Leftrightarrow & \color{red}{-1071} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-1071} & & \\\Leftrightarrow & x = \frac{-211}{1071} & & \\ & V = \left\{ \frac{-211}{1071} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{385x} +99 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+84} \\\Leftrightarrow & 924x-385x& = & 99+84 \\\Leftrightarrow & \color{red}{539} x& = & 183 \\\Leftrightarrow & x = \frac{183}{539} & & \\ & V = \left\{ \frac{183}{539} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -6x+\frac{8}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+56} & = & \color{red}{-539x} +88 \\\Leftrightarrow & -462x \color{red}{+56} \color{blue}{-56} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{-56} \\\Leftrightarrow & -462x+539x& = & 88-56 \\\Leftrightarrow & \color{red}{77} x& = & 32 \\\Leftrightarrow & x = \frac{32}{77} & & \\ & V = \left\{ \frac{32}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-36} & = & \color{red}{105x} +56 \\\Leftrightarrow & -252x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -252x-105x& = & 56+36 \\\Leftrightarrow & \color{red}{-357} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-357} & & \\\Leftrightarrow & x = \frac{-92}{357} & & \\ & V = \left\{ \frac{-92}{357} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 20x-\frac{10}{3}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-20} & = & \color{red}{42x} +7 \\\Leftrightarrow & 120x \color{red}{-20} \color{blue}{+20} \color{blue}{-42x} & = & \color{red}{42x} +7 \color{blue}{-42x} \color{blue}{+20} \\\Leftrightarrow & 120x-42x& = & 7+20 \\\Leftrightarrow & \color{red}{78} x& = & 27 \\\Leftrightarrow & x = \frac{27}{78} & & \\\Leftrightarrow & x = \frac{9}{26} & & \\ & V = \left\{ \frac{9}{26} \right\} & \\\end{align}\)