Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{11})& = & 6x+\frac{8}{3} \\\Leftrightarrow & 25x+\frac{25}{11}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+75} & = & \color{red}{198x} +88 \\\Leftrightarrow & 825x \color{red}{+75} \color{blue}{-75} \color{blue}{-198x} & = & \color{red}{198x} +88 \color{blue}{-198x} \color{blue}{-75} \\\Leftrightarrow & 825x-198x& = & 88-75 \\\Leftrightarrow & \color{red}{627} x& = & 13 \\\Leftrightarrow & x = \frac{13}{627} & & \\ & V = \left\{ \frac{13}{627} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 280x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{105} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{105} & & \\ & V = \left\{ \frac{-74}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{9})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{10}{9}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+50} & = & \color{red}{-180x} +54 \\\Leftrightarrow & -675x \color{red}{+50} \color{blue}{-50} \color{blue}{+180x} & = & \color{red}{-180x} +54 \color{blue}{+180x} \color{blue}{-50} \\\Leftrightarrow & -675x+180x& = & 54-50 \\\Leftrightarrow & \color{red}{-495} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-495} & & \\\Leftrightarrow & x = \frac{-4}{495} & & \\ & V = \left\{ \frac{-4}{495} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-540}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -540x \color{red}{-72} & = & \color{red}{90x} +25 \\\Leftrightarrow & -540x \color{red}{-72} \color{blue}{+72} \color{blue}{-90x} & = & \color{red}{90x} +25 \color{blue}{-90x} \color{blue}{+72} \\\Leftrightarrow & -540x-90x& = & 25+72 \\\Leftrightarrow & \color{red}{-630} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-630} & & \\\Leftrightarrow & x = \frac{-97}{630} & & \\ & V = \left\{ \frac{-97}{630} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+48} \\\Leftrightarrow & -336x+147x& = & 28+48 \\\Leftrightarrow & \color{red}{-189} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-189} & & \\\Leftrightarrow & x = \frac{-76}{189} & & \\ & V = \left\{ \frac{-76}{189} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{2})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{15}{2}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+135} & = & \color{red}{-126x} +4 \\\Leftrightarrow & 270x \color{red}{+135} \color{blue}{-135} \color{blue}{+126x} & = & \color{red}{-126x} +4 \color{blue}{+126x} \color{blue}{-135} \\\Leftrightarrow & 270x+126x& = & 4-135 \\\Leftrightarrow & \color{red}{396} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{396} & & \\ & V = \left\{ \frac{-131}{396} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-90} & = & \color{red}{231x} +22 \\\Leftrightarrow & -990x \color{red}{-90} \color{blue}{+90} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+90} \\\Leftrightarrow & -990x-231x& = & 22+90 \\\Leftrightarrow & \color{red}{-1221} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-1221} & & \\\Leftrightarrow & x = \frac{-112}{1221} & & \\ & V = \left\{ \frac{-112}{1221} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{7})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 6x-\frac{9}{7}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{81}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-81} & = & \color{red}{-315x} +49 \\\Leftrightarrow & 378x \color{red}{-81} \color{blue}{+81} \color{blue}{+315x} & = & \color{red}{-315x} +49 \color{blue}{+315x} \color{blue}{+81} \\\Leftrightarrow & 378x+315x& = & 49+81 \\\Leftrightarrow & \color{red}{693} x& = & 130 \\\Leftrightarrow & x = \frac{130}{693} & & \\ & V = \left\{ \frac{130}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -2x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -2x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-132} & = & \color{red}{-110x} +35 \\\Leftrightarrow & 825x \color{red}{-132} \color{blue}{+132} \color{blue}{+110x} & = & \color{red}{-110x} +35 \color{blue}{+110x} \color{blue}{+132} \\\Leftrightarrow & 825x+110x& = & 35+132 \\\Leftrightarrow & \color{red}{935} x& = & 167 \\\Leftrightarrow & x = \frac{167}{935} & & \\ & V = \left\{ \frac{167}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{2})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{25}{2}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{75}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{54x} +16 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{-54x} & = & \color{red}{54x} +16 \color{blue}{-54x} \color{blue}{-75} \\\Leftrightarrow & -120x-54x& = & 16-75 \\\Leftrightarrow & \color{red}{-174} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-174} & & \\\Leftrightarrow & x = \frac{59}{174} & & \\ & V = \left\{ \frac{59}{174} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+88} & = & \color{red}{297x} +30 \\\Leftrightarrow & 528x \color{red}{+88} \color{blue}{-88} \color{blue}{-297x} & = & \color{red}{297x} +30 \color{blue}{-297x} \color{blue}{-88} \\\Leftrightarrow & 528x-297x& = & 30-88 \\\Leftrightarrow & \color{red}{231} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{231} & & \\ & V = \left\{ \frac{-58}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 56-18 \\\Leftrightarrow & \color{red}{-273} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-273} & & \\\Leftrightarrow & x = \frac{-38}{273} & & \\ & V = \left\{ \frac{-38}{273} \right\} & \\\end{align}\)