Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & -2x+\frac{5}{8} \\\Leftrightarrow & 35x-\frac{21}{11}& = & -2x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{168}{ \color{blue}{88} })& = & (\frac{-176}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-168} & = & \color{red}{-176x} +55 \\\Leftrightarrow & 3080x \color{red}{-168} \color{blue}{+168} \color{blue}{+176x} & = & \color{red}{-176x} +55 \color{blue}{+176x} \color{blue}{+168} \\\Leftrightarrow & 3080x+176x& = & 55+168 \\\Leftrightarrow & \color{red}{3256} x& = & 223 \\\Leftrightarrow & x = \frac{223}{3256} & & \\ & V = \left\{ \frac{223}{3256} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+16} & = & \color{red}{30x} +35 \\\Leftrightarrow & -80x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +35 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & -80x-30x& = & 35-16 \\\Leftrightarrow & \color{red}{-110} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-110} & & \\\Leftrightarrow & x = \frac{-19}{110} & & \\ & V = \left\{ \frac{-19}{110} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{11})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+105} & = & \color{red}{132x} +88 \\\Leftrightarrow & -1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-132x} & = & \color{red}{132x} +88 \color{blue}{-132x} \color{blue}{-105} \\\Leftrightarrow & -1155x-132x& = & 88-105 \\\Leftrightarrow & \color{red}{-1287} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1287} & & \\\Leftrightarrow & x = \frac{17}{1287} & & \\ & V = \left\{ \frac{17}{1287} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{11})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -28x+\frac{14}{11}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x+ \frac{70}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{+70} & = & \color{red}{-495x} +44 \\\Leftrightarrow & -1540x \color{red}{+70} \color{blue}{-70} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-70} \\\Leftrightarrow & -1540x+495x& = & 44-70 \\\Leftrightarrow & \color{red}{-1045} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1045} & & \\\Leftrightarrow & x = \frac{26}{1045} & & \\ & V = \left\{ \frac{26}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -6x+\frac{15}{2}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+105} & = & \color{red}{-98x} +16 \\\Leftrightarrow & -84x \color{red}{+105} \color{blue}{-105} \color{blue}{+98x} & = & \color{red}{-98x} +16 \color{blue}{+98x} \color{blue}{-105} \\\Leftrightarrow & -84x+98x& = & 16-105 \\\Leftrightarrow & \color{red}{14} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{14} & & \\ & V = \left\{ \frac{-89}{14} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{10}{7}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{28}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+20} & = & \color{red}{28x} +21 \\\Leftrightarrow & 210x \color{red}{+20} \color{blue}{-20} \color{blue}{-28x} & = & \color{red}{28x} +21 \color{blue}{-28x} \color{blue}{-20} \\\Leftrightarrow & 210x-28x& = & 21-20 \\\Leftrightarrow & \color{red}{182} x& = & 1 \\\Leftrightarrow & x = \frac{1}{182} & & \\ & V = \left\{ \frac{1}{182} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+70} \\\Leftrightarrow & 420x+75x& = & 18+70 \\\Leftrightarrow & \color{red}{495} x& = & 88 \\\Leftrightarrow & x = \frac{88}{495} & & \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{8})& = & 6x+\frac{10}{11} \\\Leftrightarrow & 35x-\frac{35}{8}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-385} & = & \color{red}{528x} +80 \\\Leftrightarrow & 3080x \color{red}{-385} \color{blue}{+385} \color{blue}{-528x} & = & \color{red}{528x} +80 \color{blue}{-528x} \color{blue}{+385} \\\Leftrightarrow & 3080x-528x& = & 80+385 \\\Leftrightarrow & \color{red}{2552} x& = & 465 \\\Leftrightarrow & x = \frac{465}{2552} & & \\ & V = \left\{ \frac{465}{2552} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{11})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+70} & = & \color{red}{-385x} +55 \\\Leftrightarrow & 462x \color{red}{+70} \color{blue}{-70} \color{blue}{+385x} & = & \color{red}{-385x} +55 \color{blue}{+385x} \color{blue}{-70} \\\Leftrightarrow & 462x+385x& = & 55-70 \\\Leftrightarrow & \color{red}{847} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{847} & & \\ & V = \left\{ \frac{-15}{847} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{7})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{12}{7}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-132} & = & \color{red}{-308x} +42 \\\Leftrightarrow & -1155x \color{red}{-132} \color{blue}{+132} \color{blue}{+308x} & = & \color{red}{-308x} +42 \color{blue}{+308x} \color{blue}{+132} \\\Leftrightarrow & -1155x+308x& = & 42+132 \\\Leftrightarrow & \color{red}{-847} x& = & 174 \\\Leftrightarrow & x = \frac{174}{-847} & & \\\Leftrightarrow & x = \frac{-174}{847} & & \\ & V = \left\{ \frac{-174}{847} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+132} & = & \color{red}{495x} +50 \\\Leftrightarrow & -990x \color{red}{+132} \color{blue}{-132} \color{blue}{-495x} & = & \color{red}{495x} +50 \color{blue}{-495x} \color{blue}{-132} \\\Leftrightarrow & -990x-495x& = & 50-132 \\\Leftrightarrow & \color{red}{-1485} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-1485} & & \\\Leftrightarrow & x = \frac{82}{1485} & & \\ & V = \left\{ \frac{82}{1485} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{9})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -25x+\frac{20}{9}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+140} & = & \color{red}{-252x} +36 \\\Leftrightarrow & -1575x \color{red}{+140} \color{blue}{-140} \color{blue}{+252x} & = & \color{red}{-252x} +36 \color{blue}{+252x} \color{blue}{-140} \\\Leftrightarrow & -1575x+252x& = & 36-140 \\\Leftrightarrow & \color{red}{-1323} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1323} & & \\\Leftrightarrow & x = \frac{104}{1323} & & \\ & V = \left\{ \frac{104}{1323} \right\} & \\\end{align}\)