Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x-1)& = & -12 \color{red}{+} (-14-5x) \\\Leftrightarrow & -6x-6& = &-12-14-5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-26 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-26 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -6x+5x& = &-26+6 \\\Leftrightarrow & -x& = &-20 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-20}{ \color{red}{-1} } \\\Leftrightarrow & x = 20 & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-2)& = & -5 \color{red}{-} (-9-5x) \\\Leftrightarrow & -6x-6& = &-5+9+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &4 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &4+6 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x-1)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & 30x-6& = &13+14+x \\\Leftrightarrow & 30x \color{red}{-6} & = &27 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &27+6 \\\Leftrightarrow & 29x& = &33 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{33}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-4)& = & -7 \color{red}{+} (13+x) \\\Leftrightarrow & -6x-24& = &-7+13+x \\\Leftrightarrow & -6x \color{red}{-24} & = &6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -6x-x& = &6+24 \\\Leftrightarrow & -7x& = &30 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{30}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-4)& = & -7 \color{red}{-} (-8+x) \\\Leftrightarrow & 4x-8& = &-7+8-x \\\Leftrightarrow & 4x \color{red}{-8} & = &1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 4x+x& = &1+8 \\\Leftrightarrow & 5x& = &9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-6)& = & 2 \color{red}{-} (2+4x) \\\Leftrightarrow & 3x-18& = &2-2-4x \\\Leftrightarrow & 3x \color{red}{-18} & = &0 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & 3x+4x& = &0+18 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-2)& = & 14 \color{red}{-} (-4-5x) \\\Leftrightarrow & -36x-12& = &14+4+5x \\\Leftrightarrow & -36x \color{red}{-12} & = &18 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -36x-5x& = &18+12 \\\Leftrightarrow & -41x& = &30 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{30}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-30}{41} & & \\ & V = \left\{ \frac{-30}{41} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+1)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & -10x+5& = &-14+10+x \\\Leftrightarrow & -10x \color{red}{+5} & = &-4 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -10x-x& = &-4-5 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+4)& = & -13 \color{red}{-} (-14+2x) \\\Leftrightarrow & -5x+20& = &-13+14-2x \\\Leftrightarrow & -5x \color{red}{+20} & = &1 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -5x+2x& = &1-20 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-4)& = & 10 \color{red}{+} (4+x) \\\Leftrightarrow & 8x-16& = &10+4+x \\\Leftrightarrow & 8x \color{red}{-16} & = &14 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 8x-x& = &14+16 \\\Leftrightarrow & 7x& = &30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{30}{7} & & \\ & V = \left\{ \frac{30}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+1)& = & -14 \color{red}{-} (4+x) \\\Leftrightarrow & -25x+5& = &-14-4-x \\\Leftrightarrow & -25x \color{red}{+5} & = &-18 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -25x+x& = &-18-5 \\\Leftrightarrow & -24x& = &-23 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-23}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{23}{24} & & \\ & V = \left\{ \frac{23}{24} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+4)& = & -6 \color{red}{-} (-13+x) \\\Leftrightarrow & -25x+20& = &-6+13-x \\\Leftrightarrow & -25x \color{red}{+20} & = &7 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -25x+x& = &7-20 \\\Leftrightarrow & -24x& = &-13 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-13}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{13}{24} & & \\ & V = \left\{ \frac{13}{24} \right\} & \\\end{align}\)