Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 60x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{10} & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{6})& = & -4x+\frac{9}{5} \\\Leftrightarrow & 21x+\frac{35}{6}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-120}{ \color{blue}{30} }x+ \frac{54}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{+175} & = & \color{red}{-120x} +54 \\\Leftrightarrow & 630x \color{red}{+175} \color{blue}{-175} \color{blue}{+120x} & = & \color{red}{-120x} +54 \color{blue}{+120x} \color{blue}{-175} \\\Leftrightarrow & 630x+120x& = & 54-175 \\\Leftrightarrow & \color{red}{750} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{750} & & \\ & V = \left\{ \frac{-121}{750} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{189x} +56 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{+90} \\\Leftrightarrow & 630x-189x& = & 56+90 \\\Leftrightarrow & \color{red}{441} x& = & 146 \\\Leftrightarrow & x = \frac{146}{441} & & \\ & V = \left\{ \frac{146}{441} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{16}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{48}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{-105x} +40 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{+48} \\\Leftrightarrow & 180x+105x& = & 40+48 \\\Leftrightarrow & \color{red}{285} x& = & 88 \\\Leftrightarrow & x = \frac{88}{285} & & \\ & V = \left\{ \frac{88}{285} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+105} & = & \color{red}{196x} +36 \\\Leftrightarrow & -168x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +36 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & -168x-196x& = & 36-105 \\\Leftrightarrow & \color{red}{-364} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-364} & & \\\Leftrightarrow & x = \frac{69}{364} & & \\ & V = \left\{ \frac{69}{364} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 60x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-16} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & 84x+35x& = & 10+16 \\\Leftrightarrow & \color{red}{119} x& = & 26 \\\Leftrightarrow & x = \frac{26}{119} & & \\ & V = \left\{ \frac{26}{119} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 24x-\frac{24}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{336}{ \color{blue}{14} }x- \frac{48}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+48} \\\Leftrightarrow & 336x+70x& = & 63+48 \\\Leftrightarrow & \color{red}{406} x& = & 111 \\\Leftrightarrow & x = \frac{111}{406} & & \\ & V = \left\{ \frac{111}{406} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{11})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{25}{11}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-75} & = & \color{red}{99x} +22 \\\Leftrightarrow & -825x \color{red}{-75} \color{blue}{+75} \color{blue}{-99x} & = & \color{red}{99x} +22 \color{blue}{-99x} \color{blue}{+75} \\\Leftrightarrow & -825x-99x& = & 22+75 \\\Leftrightarrow & \color{red}{-924} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-924} & & \\\Leftrightarrow & x = \frac{-97}{924} & & \\ & V = \left\{ \frac{-97}{924} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & 4x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{15}{7}& = & 4x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+165} & = & \color{red}{308x} +56 \\\Leftrightarrow & 693x \color{red}{+165} \color{blue}{-165} \color{blue}{-308x} & = & \color{red}{308x} +56 \color{blue}{-308x} \color{blue}{-165} \\\Leftrightarrow & 693x-308x& = & 56-165 \\\Leftrightarrow & \color{red}{385} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{385} & & \\ & V = \left\{ \frac{-109}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-4} & = & \color{red}{63x} +30 \\\Leftrightarrow & -54x \color{red}{-4} \color{blue}{+4} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+4} \\\Leftrightarrow & -54x-63x& = & 30+4 \\\Leftrightarrow & \color{red}{-117} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-117} & & \\\Leftrightarrow & x = \frac{-34}{117} & & \\ & V = \left\{ \frac{-34}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{-16} & = & \color{red}{-54x} +7 \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{+16} \\\Leftrightarrow & 24x+54x& = & 7+16 \\\Leftrightarrow & \color{red}{78} x& = & 23 \\\Leftrightarrow & x = \frac{23}{78} & & \\ & V = \left\{ \frac{23}{78} \right\} & \\\end{align}\)