Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-6x-2)=-12+(12+x)\)
2. \(5(5x+5)=5+(14+x)\)
3. \(4(-2x-5)=10-(4-5x)\)
4. \(3(4x-1)=4-(8+x)\)
5. \(3(-3x+6)=12+(12+x)\)
6. \(5(4x-7)=-5+(-9+3x)\)
7. \(4(4x+4)=-8-(-15-3x)\)
8. \(2(-2x-5)=3-(5-3x)\)
9. \(6(x+2)=1+(-13+x)\)
10. \(2(-2x-4)=-2-(-10-3x)\)
11. \(6(-2x+3)=10-(1+x)\)
12. \(4(-3x+1)=-3-(-11+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-2)& = & -12 \color{red}{+} (12+x) \\\Leftrightarrow & -12x-4& = &-12+12+x \\\Leftrightarrow & -12x \color{red}{-4} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &0+4 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+5)& = & 5 \color{red}{+} (14+x) \\\Leftrightarrow & 25x+25& = &5+14+x \\\Leftrightarrow & 25x \color{red}{+25} & = &19 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 25x-x& = &19-25 \\\Leftrightarrow & 24x& = &-6 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-6}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x-5)& = & 10 \color{red}{-} (4-5x) \\\Leftrightarrow & -8x-20& = &10-4+5x \\\Leftrightarrow & -8x \color{red}{-20} & = &6 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & -8x-5x& = &6+20 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-1)& = & 4 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-3& = &4-8-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-4+3 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+6)& = & 12 \color{red}{+} (12+x) \\\Leftrightarrow & -9x+18& = &12+12+x \\\Leftrightarrow & -9x \color{red}{+18} & = &24 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -9x-x& = &24-18 \\\Leftrightarrow & -10x& = &6 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{6}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x-7)& = & -5 \color{red}{+} (-9+3x) \\\Leftrightarrow & 20x-35& = &-5-9+3x \\\Leftrightarrow & 20x \color{red}{-35} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 20x-3x& = &-14+35 \\\Leftrightarrow & 17x& = &21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x+4)& = & -8 \color{red}{-} (-15-3x) \\\Leftrightarrow & 16x+16& = &-8+15+3x \\\Leftrightarrow & 16x \color{red}{+16} & = &7 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 16x-3x& = &7-16 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x-5)& = & 3 \color{red}{-} (5-3x) \\\Leftrightarrow & -4x-10& = &3-5+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &-2+10 \\\Leftrightarrow & -7x& = &8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x+2)& = & 1 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x+12& = &1-13+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-12-12 \\\Leftrightarrow & 5x& = &-24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-4)& = & -2 \color{red}{-} (-10-3x) \\\Leftrightarrow & -4x-8& = &-2+10+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &8+8 \\\Leftrightarrow & -7x& = &16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+3)& = & 10 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+18& = &10-1-x \\\Leftrightarrow & -12x \color{red}{+18} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &9-18 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+1)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & -12x+4& = &-3+11-x \\\Leftrightarrow & -12x \color{red}{+4} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &8-4 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)