Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-4)& = & 7 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-24& = &7-7-x \\\Leftrightarrow & -12x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &0+24 \\\Leftrightarrow & -11x& = &24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-2)& = & -2 \color{red}{+} (10-5x) \\\Leftrightarrow & 8x-8& = &-2+10-5x \\\Leftrightarrow & 8x \color{red}{-8} & = &8 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 8x+5x& = &8+8 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+4)& = & 5 \color{red}{-} (4+x) \\\Leftrightarrow & 10x+8& = &5-4-x \\\Leftrightarrow & 10x \color{red}{+8} & = &1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 10x+x& = &1-8 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x-3)& = & -4 \color{red}{+} (12-2x) \\\Leftrightarrow & 15x-9& = &-4+12-2x \\\Leftrightarrow & 15x \color{red}{-9} & = &8 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 15x+2x& = &8+9 \\\Leftrightarrow & 17x& = &17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{17}{ \color{red}{17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+7)& = & -15 \color{red}{+} (11+x) \\\Leftrightarrow & -24x+28& = &-15+11+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-4-28 \\\Leftrightarrow & -25x& = &-32 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-32}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{32}{25} & & \\ & V = \left\{ \frac{32}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+4)& = & -1 \color{red}{-} (-14-2x) \\\Leftrightarrow & 9x+12& = &-1+14+2x \\\Leftrightarrow & 9x \color{red}{+12} & = &13 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & 9x-2x& = &13-12 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x-6)& = & -3 \color{red}{-} (7-2x) \\\Leftrightarrow & 15x-18& = &-3-7+2x \\\Leftrightarrow & 15x \color{red}{-18} & = &-10 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & 15x-2x& = &-10+18 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-1)& = & -9 \color{red}{-} (-4+x) \\\Leftrightarrow & 2x-2& = &-9+4-x \\\Leftrightarrow & 2x \color{red}{-2} & = &-5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 2x+x& = &-5+2 \\\Leftrightarrow & 3x& = &-3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-3}{ \color{red}{3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+6)& = & 8 \color{red}{-} (1+4x) \\\Leftrightarrow & 5x+30& = &8-1-4x \\\Leftrightarrow & 5x \color{red}{+30} & = &7 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 5x+4x& = &7-30 \\\Leftrightarrow & 9x& = &-23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-23}{9} & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x+3)& = & 3 \color{red}{+} (9+x) \\\Leftrightarrow & -12x+18& = &3+9+x \\\Leftrightarrow & -12x \color{red}{+18} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &12-18 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-7)& = & 13 \color{red}{+} (-12-5x) \\\Leftrightarrow & 6x-42& = &13-12-5x \\\Leftrightarrow & 6x \color{red}{-42} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 6x+5x& = &1+42 \\\Leftrightarrow & 11x& = &43 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{43}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{43}{11} & & \\ & V = \left\{ \frac{43}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-2)& = & -10 \color{red}{+} (4+3x) \\\Leftrightarrow & 5x-10& = &-10+4+3x \\\Leftrightarrow & 5x \color{red}{-10} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 5x-3x& = &-6+10 \\\Leftrightarrow & 2x& = &4 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{4}{ \color{red}{2} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)