Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & -990x+231x& = & 22-54 \\\Leftrightarrow & \color{red}{-759} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-759} & & \\\Leftrightarrow & x = \frac{32}{759} & & \\ & V = \left\{ \frac{32}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x+\frac{9}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+63} & = & \color{red}{175x} +40 \\\Leftrightarrow & 210x \color{red}{+63} \color{blue}{-63} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{-63} \\\Leftrightarrow & 210x-175x& = & 40-63 \\\Leftrightarrow & \color{red}{35} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{35} & & \\ & V = \left\{ \frac{-23}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 4x+\frac{10}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+50} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 220x \color{red}{+50} \color{blue}{-50} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-50} \\\Leftrightarrow & 220x+385x& = & 22-50 \\\Leftrightarrow & \color{red}{605} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{605} & & \\ & V = \left\{ \frac{-28}{605} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-105} & = & \color{red}{56x} +32 \\\Leftrightarrow & 420x \color{red}{-105} \color{blue}{+105} \color{blue}{-56x} & = & \color{red}{56x} +32 \color{blue}{-56x} \color{blue}{+105} \\\Leftrightarrow & 420x-56x& = & 32+105 \\\Leftrightarrow & \color{red}{364} x& = & 137 \\\Leftrightarrow & x = \frac{137}{364} & & \\ & V = \left\{ \frac{137}{364} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{3})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{-18x} +21 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{+18x} & = & \color{red}{-18x} +21 \color{blue}{+18x} \color{blue}{+40} \\\Leftrightarrow & -120x+18x& = & 21+40 \\\Leftrightarrow & \color{red}{-102} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-102} & & \\\Leftrightarrow & x = \frac{-61}{102} & & \\ & V = \left\{ \frac{-61}{102} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{11})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -25x+\frac{15}{11}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+105} & = & \color{red}{693x} +44 \\\Leftrightarrow & -1925x \color{red}{+105} \color{blue}{-105} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-105} \\\Leftrightarrow & -1925x-693x& = & 44-105 \\\Leftrightarrow & \color{red}{-2618} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-2618} & & \\\Leftrightarrow & x = \frac{61}{2618} & & \\ & V = \left\{ \frac{61}{2618} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{3})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{25}{3}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+275} & = & \color{red}{-297x} +12 \\\Leftrightarrow & 660x \color{red}{+275} \color{blue}{-275} \color{blue}{+297x} & = & \color{red}{-297x} +12 \color{blue}{+297x} \color{blue}{-275} \\\Leftrightarrow & 660x+297x& = & 12-275 \\\Leftrightarrow & \color{red}{957} x& = & -263 \\\Leftrightarrow & x = \frac{-263}{957} & & \\ & V = \left\{ \frac{-263}{957} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{6})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 14x+\frac{35}{6}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{12}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{150x} +12 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{-150x} & = & \color{red}{150x} +12 \color{blue}{-150x} \color{blue}{-175} \\\Leftrightarrow & 420x-150x& = & 12-175 \\\Leftrightarrow & \color{red}{270} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{270} & & \\ & V = \left\{ \frac{-163}{270} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -4x-\frac{8}{9}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-8} & = & \color{red}{45x} +10 \\\Leftrightarrow & -36x \color{red}{-8} \color{blue}{+8} \color{blue}{-45x} & = & \color{red}{45x} +10 \color{blue}{-45x} \color{blue}{+8} \\\Leftrightarrow & -36x-45x& = & 10+8 \\\Leftrightarrow & \color{red}{-81} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-81} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+1)& = & -7x+\frac{5}{7} \\\Leftrightarrow & -10x-5& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{35}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-35} & = & \color{red}{-49x} +5 \\\Leftrightarrow & -70x \color{red}{-35} \color{blue}{+35} \color{blue}{+49x} & = & \color{red}{-49x} +5 \color{blue}{+49x} \color{blue}{+35} \\\Leftrightarrow & -70x+49x& = & 5+35 \\\Leftrightarrow & \color{red}{-21} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-21} & & \\\Leftrightarrow & x = \frac{-40}{21} & & \\ & V = \left\{ \frac{-40}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 2x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-54} & = & \color{red}{66x} +44 \\\Leftrightarrow & -594x \color{red}{-54} \color{blue}{+54} \color{blue}{-66x} & = & \color{red}{66x} +44 \color{blue}{-66x} \color{blue}{+54} \\\Leftrightarrow & -594x-66x& = & 44+54 \\\Leftrightarrow & \color{red}{-660} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-660} & & \\\Leftrightarrow & x = \frac{-49}{330} & & \\ & V = \left\{ \frac{-49}{330} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{2})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{25}{2}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{+275} & = & \color{red}{-66x} +10 \\\Leftrightarrow & -440x \color{red}{+275} \color{blue}{-275} \color{blue}{+66x} & = & \color{red}{-66x} +10 \color{blue}{+66x} \color{blue}{-275} \\\Leftrightarrow & -440x+66x& = & 10-275 \\\Leftrightarrow & \color{red}{-374} x& = & -265 \\\Leftrightarrow & x = \frac{-265}{-374} & & \\\Leftrightarrow & x = \frac{265}{374} & & \\ & V = \left\{ \frac{265}{374} \right\} & \\\end{align}\)