Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-200} & = & \color{red}{270x} +27 \\\Leftrightarrow & 600x \color{red}{-200} \color{blue}{+200} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+200} \\\Leftrightarrow & 600x-270x& = & 27+200 \\\Leftrightarrow & \color{red}{330} x& = & 227 \\\Leftrightarrow & x = \frac{227}{330} & & \\ & V = \left\{ \frac{227}{330} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+154} & = & \color{red}{-99x} +18 \\\Leftrightarrow & -462x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & -462x+99x& = & 18-154 \\\Leftrightarrow & \color{red}{-363} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-363} & & \\\Leftrightarrow & x = \frac{136}{363} & & \\ & V = \left\{ \frac{136}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{-225x} +63 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{+225x} & = & \color{red}{-225x} +63 \color{blue}{+225x} \color{blue}{-20} \\\Leftrightarrow & -180x+225x& = & 63-20 \\\Leftrightarrow & \color{red}{45} x& = & 43 \\\Leftrightarrow & x = \frac{43}{45} & & \\ & V = \left\{ \frac{43}{45} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{4})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -14x+\frac{21}{4}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x+ \frac{189}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+189} & = & \color{red}{108x} +8 \\\Leftrightarrow & -504x \color{red}{+189} \color{blue}{-189} \color{blue}{-108x} & = & \color{red}{108x} +8 \color{blue}{-108x} \color{blue}{-189} \\\Leftrightarrow & -504x-108x& = & 8-189 \\\Leftrightarrow & \color{red}{-612} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{-612} & & \\\Leftrightarrow & x = \frac{181}{612} & & \\ & V = \left\{ \frac{181}{612} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+72} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 594x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 594x+165x& = & 88-72 \\\Leftrightarrow & \color{red}{759} x& = & 16 \\\Leftrightarrow & x = \frac{16}{759} & & \\ & V = \left\{ \frac{16}{759} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{9})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{9}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+16} & = & \color{red}{45x} +12 \\\Leftrightarrow & -108x \color{red}{+16} \color{blue}{-16} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-16} \\\Leftrightarrow & -108x-45x& = & 12-16 \\\Leftrightarrow & \color{red}{-153} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-153} & & \\\Leftrightarrow & x = \frac{4}{153} & & \\ & V = \left\{ \frac{4}{153} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & -168x+35x& = & 2-30 \\\Leftrightarrow & \color{red}{-133} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-133} & & \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & -360x+105x& = & 40+54 \\\Leftrightarrow & \color{red}{-255} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-255} & & \\\Leftrightarrow & x = \frac{-94}{255} & & \\ & V = \left\{ \frac{-94}{255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{-48} & = & \color{red}{140x} +15 \\\Leftrightarrow & -320x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +15 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & -320x-140x& = & 15+48 \\\Leftrightarrow & \color{red}{-460} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-460} & & \\\Leftrightarrow & x = \frac{-63}{460} & & \\ & V = \left\{ \frac{-63}{460} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x-\frac{12}{11}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3960}{ \color{blue}{132} }x- \frac{144}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3960x \color{red}{-144} & = & \color{red}{-924x} +55 \\\Leftrightarrow & -3960x \color{red}{-144} \color{blue}{+144} \color{blue}{+924x} & = & \color{red}{-924x} +55 \color{blue}{+924x} \color{blue}{+144} \\\Leftrightarrow & -3960x+924x& = & 55+144 \\\Leftrightarrow & \color{red}{-3036} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-3036} & & \\\Leftrightarrow & x = \frac{-199}{3036} & & \\ & V = \left\{ \frac{-199}{3036} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{5})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-154} & = & \color{red}{-165x} +20 \\\Leftrightarrow & -1540x \color{red}{-154} \color{blue}{+154} \color{blue}{+165x} & = & \color{red}{-165x} +20 \color{blue}{+165x} \color{blue}{+154} \\\Leftrightarrow & -1540x+165x& = & 20+154 \\\Leftrightarrow & \color{red}{-1375} x& = & 174 \\\Leftrightarrow & x = \frac{174}{-1375} & & \\\Leftrightarrow & x = \frac{-174}{1375} & & \\ & V = \left\{ \frac{-174}{1375} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{4})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-105} & = & \color{red}{-196x} +40 \\\Leftrightarrow & -168x \color{red}{-105} \color{blue}{+105} \color{blue}{+196x} & = & \color{red}{-196x} +40 \color{blue}{+196x} \color{blue}{+105} \\\Leftrightarrow & -168x+196x& = & 40+105 \\\Leftrightarrow & \color{red}{28} x& = & 145 \\\Leftrightarrow & x = \frac{145}{28} & & \\ & V = \left\{ \frac{145}{28} \right\} & \\\end{align}\)