Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{28}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{+135} & = & \color{red}{-252x} +28 \\\Leftrightarrow & 720x \color{red}{+135} \color{blue}{-135} \color{blue}{+252x} & = & \color{red}{-252x} +28 \color{blue}{+252x} \color{blue}{-135} \\\Leftrightarrow & 720x+252x& = & 28-135 \\\Leftrightarrow & \color{red}{972} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{972} & & \\ & V = \left\{ \frac{-107}{972} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{8}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+16} & = & \color{red}{98x} +63 \\\Leftrightarrow & 140x \color{red}{+16} \color{blue}{-16} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{-16} \\\Leftrightarrow & 140x-98x& = & 63-16 \\\Leftrightarrow & \color{red}{42} x& = & 47 \\\Leftrightarrow & x = \frac{47}{42} & & \\ & V = \left\{ \frac{47}{42} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+150} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & -660x-275x& = & 22-150 \\\Leftrightarrow & \color{red}{-935} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-935} & & \\\Leftrightarrow & x = \frac{128}{935} & & \\ & V = \left\{ \frac{128}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-56} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 378x \color{red}{-56} \color{blue}{+56} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+56} \\\Leftrightarrow & 378x+315x& = & 54+56 \\\Leftrightarrow & \color{red}{693} x& = & 110 \\\Leftrightarrow & x = \frac{110}{693} & & \\\Leftrightarrow & x = \frac{10}{63} & & \\ & V = \left\{ \frac{10}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-28} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 350x \color{red}{-28} \color{blue}{+28} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+28} \\\Leftrightarrow & 350x+105x& = & 50+28 \\\Leftrightarrow & \color{red}{455} x& = & 78 \\\Leftrightarrow & x = \frac{78}{455} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{9})& = & 4x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{+20} & = & \color{red}{36x} +8 \\\Leftrightarrow & 135x \color{red}{+20} \color{blue}{-20} \color{blue}{-36x} & = & \color{red}{36x} +8 \color{blue}{-36x} \color{blue}{-20} \\\Leftrightarrow & 135x-36x& = & 8-20 \\\Leftrightarrow & \color{red}{99} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{99} & & \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{8}{9} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-42} & = & \color{red}{18x} +8 \\\Leftrightarrow & 189x \color{red}{-42} \color{blue}{+42} \color{blue}{-18x} & = & \color{red}{18x} +8 \color{blue}{-18x} \color{blue}{+42} \\\Leftrightarrow & 189x-18x& = & 8+42 \\\Leftrightarrow & \color{red}{171} x& = & 50 \\\Leftrightarrow & x = \frac{50}{171} & & \\ & V = \left\{ \frac{50}{171} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -18x-\frac{24}{11}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x- \frac{192}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{-192} & = & \color{red}{-792x} +77 \\\Leftrightarrow & -1584x \color{red}{-192} \color{blue}{+192} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+192} \\\Leftrightarrow & -1584x+792x& = & 77+192 \\\Leftrightarrow & \color{red}{-792} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-792} & & \\\Leftrightarrow & x = \frac{-269}{792} & & \\ & V = \left\{ \frac{-269}{792} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 18x-\frac{12}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x- \frac{120}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{-120} & = & \color{red}{-550x} +99 \\\Leftrightarrow & 1980x \color{red}{-120} \color{blue}{+120} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{+120} \\\Leftrightarrow & 1980x+550x& = & 99+120 \\\Leftrightarrow & \color{red}{2530} x& = & 219 \\\Leftrightarrow & x = \frac{219}{2530} & & \\ & V = \left\{ \frac{219}{2530} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-48} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{-48} \color{blue}{+48} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+48} \\\Leftrightarrow & 252x-105x& = & 14+48 \\\Leftrightarrow & \color{red}{147} x& = & 62 \\\Leftrightarrow & x = \frac{62}{147} & & \\ & V = \left\{ \frac{62}{147} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{8}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+72} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 378x \color{red}{+72} \color{blue}{-72} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-72} \\\Leftrightarrow & 378x+315x& = & 56-72 \\\Leftrightarrow & \color{red}{693} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{693} & & \\ & V = \left\{ \frac{-16}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+220} & = & \color{red}{-693x} +54 \\\Leftrightarrow & -1980x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & -1980x+693x& = & 54-220 \\\Leftrightarrow & \color{red}{-1287} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-1287} & & \\\Leftrightarrow & x = \frac{166}{1287} & & \\ & V = \left\{ \frac{166}{1287} \right\} & \\\end{align}\)