Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{9}{5} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+12} & = & \color{red}{20x} +9 \\\Leftrightarrow & -75x \color{red}{+12} \color{blue}{-12} \color{blue}{-20x} & = & \color{red}{20x} +9 \color{blue}{-20x} \color{blue}{-12} \\\Leftrightarrow & -75x-20x& = & 9-12 \\\Leftrightarrow & \color{red}{-95} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-95} & & \\\Leftrightarrow & x = \frac{3}{95} & & \\ & V = \left\{ \frac{3}{95} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{6}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{-12} & = & \color{red}{110x} +99 \\\Leftrightarrow & 132x \color{red}{-12} \color{blue}{+12} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{+12} \\\Leftrightarrow & 132x-110x& = & 99+12 \\\Leftrightarrow & \color{red}{22} x& = & 111 \\\Leftrightarrow & x = \frac{111}{22} & & \\ & V = \left\{ \frac{111}{22} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{5})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 14x-\frac{14}{5}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{280}{ \color{blue}{20} }x- \frac{56}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 280x \color{red}{-56} & = & \color{red}{180x} +15 \\\Leftrightarrow & 280x \color{red}{-56} \color{blue}{+56} \color{blue}{-180x} & = & \color{red}{180x} +15 \color{blue}{-180x} \color{blue}{+56} \\\Leftrightarrow & 280x-180x& = & 15+56 \\\Leftrightarrow & \color{red}{100} x& = & 71 \\\Leftrightarrow & x = \frac{71}{100} & & \\ & V = \left\{ \frac{71}{100} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{99x} +24 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-99x} & = & \color{red}{99x} +24 \color{blue}{-99x} \color{blue}{+154} \\\Leftrightarrow & -1155x-99x& = & 24+154 \\\Leftrightarrow & \color{red}{-1254} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1254} & & \\\Leftrightarrow & x = \frac{-89}{627} & & \\ & V = \left\{ \frac{-89}{627} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{275}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+275} & = & \color{red}{-297x} +90 \\\Leftrightarrow & -1980x \color{red}{+275} \color{blue}{-275} \color{blue}{+297x} & = & \color{red}{-297x} +90 \color{blue}{+297x} \color{blue}{-275} \\\Leftrightarrow & -1980x+297x& = & 90-275 \\\Leftrightarrow & \color{red}{-1683} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-1683} & & \\\Leftrightarrow & x = \frac{185}{1683} & & \\ & V = \left\{ \frac{185}{1683} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 4x+\frac{5}{2} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{126}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{56}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 126x \color{red}{-12} & = & \color{red}{56x} +35 \\\Leftrightarrow & 126x \color{red}{-12} \color{blue}{+12} \color{blue}{-56x} & = & \color{red}{56x} +35 \color{blue}{-56x} \color{blue}{+12} \\\Leftrightarrow & 126x-56x& = & 35+12 \\\Leftrightarrow & \color{red}{70} x& = & 47 \\\Leftrightarrow & x = \frac{47}{70} & & \\ & V = \left\{ \frac{47}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{+96} & = & \color{red}{200x} +45 \\\Leftrightarrow & -480x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & -480x-200x& = & 45-96 \\\Leftrightarrow & \color{red}{-680} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-680} & & \\\Leftrightarrow & x = \frac{3}{40} & & \\ & V = \left\{ \frac{3}{40} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{245x} +40 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{-42} \\\Leftrightarrow & -210x-245x& = & 40-42 \\\Leftrightarrow & \color{red}{-455} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-455} & & \\\Leftrightarrow & x = \frac{2}{455} & & \\ & V = \left\{ \frac{2}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{15}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-378}{ \color{blue}{42} }x- \frac{90}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -378x \color{red}{-90} & = & \color{red}{210x} +35 \\\Leftrightarrow & -378x \color{red}{-90} \color{blue}{+90} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+90} \\\Leftrightarrow & -378x-210x& = & 35+90 \\\Leftrightarrow & \color{red}{-588} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-588} & & \\\Leftrightarrow & x = \frac{-125}{588} & & \\ & V = \left\{ \frac{-125}{588} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{-180} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 1980x \color{red}{-180} \color{blue}{+180} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{+180} \\\Leftrightarrow & 1980x+550x& = & 33+180 \\\Leftrightarrow & \color{red}{2530} x& = & 213 \\\Leftrightarrow & x = \frac{213}{2530} & & \\ & V = \left\{ \frac{213}{2530} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{7})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+132} & = & \color{red}{385x} +70 \\\Leftrightarrow & 924x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +70 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 924x-385x& = & 70-132 \\\Leftrightarrow & \color{red}{539} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{539} & & \\ & V = \left\{ \frac{-62}{539} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{35}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-70} & = & \color{red}{18x} +27 \\\Leftrightarrow & 84x \color{red}{-70} \color{blue}{+70} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{+70} \\\Leftrightarrow & 84x-18x& = & 27+70 \\\Leftrightarrow & \color{red}{66} x& = & 97 \\\Leftrightarrow & x = \frac{97}{66} & & \\ & V = \left\{ \frac{97}{66} \right\} & \\\end{align}\)