Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-4x+2)=6+(-11-5x)\)
2. \(3(4x-4)=9+(-5+x)\)
3. \(6(2x-3)=4-(2+x)\)
4. \(2(-2x-1)=-9-(-13+x)\)
5. \(4(3x+1)=3-(-5+x)\)
6. \(5(5x-3)=14+(-14-4x)\)
7. \(6(-x+4)=2-(13-5x)\)
8. \(2(-3x-6)=-10-(9-5x)\)
9. \(6(3x-7)=-7+(5-5x)\)
10. \(3(-6x+1)=-9+(-5+x)\)
11. \(6(-4x+2)=-7+(14+x)\)
12. \(5(-3x-4)=-7-(9-2x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+2)& = & 6 \color{red}{+} (-11-5x) \\\Leftrightarrow & -8x+4& = &6-11-5x \\\Leftrightarrow & -8x \color{red}{+4} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -8x+5x& = &-5-4 \\\Leftrightarrow & -3x& = &-9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-9}{ \color{red}{-3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-4)& = & 9 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x-12& = &9-5+x \\\Leftrightarrow & 12x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &4+12 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x-3)& = & 4 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-18& = &4-2-x \\\Leftrightarrow & 12x \color{red}{-18} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &2+18 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-1)& = & -9 \color{red}{-} (-13+x) \\\Leftrightarrow & -4x-2& = &-9+13-x \\\Leftrightarrow & -4x \color{red}{-2} & = &4 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -4x+x& = &4+2 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+1)& = & 3 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x+4& = &3+5-x \\\Leftrightarrow & 12x \color{red}{+4} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &8-4 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-3)& = & 14 \color{red}{+} (-14-4x) \\\Leftrightarrow & 25x-15& = &14-14-4x \\\Leftrightarrow & 25x \color{red}{-15} & = &0 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 25x+4x& = &0+15 \\\Leftrightarrow & 29x& = &15 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{15}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{15}{29} & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x+4)& = & 2 \color{red}{-} (13-5x) \\\Leftrightarrow & -6x+24& = &2-13+5x \\\Leftrightarrow & -6x \color{red}{+24} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -6x-5x& = &-11-24 \\\Leftrightarrow & -11x& = &-35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-6)& = & -10 \color{red}{-} (9-5x) \\\Leftrightarrow & -6x-12& = &-10-9+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-19 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &-19+12 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-7)& = & -7 \color{red}{+} (5-5x) \\\Leftrightarrow & 18x-42& = &-7+5-5x \\\Leftrightarrow & 18x \color{red}{-42} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 18x+5x& = &-2+42 \\\Leftrightarrow & 23x& = &40 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{40}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{40}{23} & & \\ & V = \left\{ \frac{40}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+1)& = & -9 \color{red}{+} (-5+x) \\\Leftrightarrow & -18x+3& = &-9-5+x \\\Leftrightarrow & -18x \color{red}{+3} & = &-14 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -18x-x& = &-14-3 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+2)& = & -7 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+12& = &-7+14+x \\\Leftrightarrow & -24x \color{red}{+12} & = &7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &7-12 \\\Leftrightarrow & -25x& = &-5 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-5}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x-4)& = & -7 \color{red}{-} (9-2x) \\\Leftrightarrow & -15x-20& = &-7-9+2x \\\Leftrightarrow & -15x \color{red}{-20} & = &-16 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & -15x-2x& = &-16+20 \\\Leftrightarrow & -17x& = &4 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{4}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)