Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x-6)& = & 3 \color{red}{+} (12+x) \\\Leftrightarrow & 30x-30& = &3+12+x \\\Leftrightarrow & 30x \color{red}{-30} & = &15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &15+30 \\\Leftrightarrow & 29x& = &45 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{45}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{45}{29} & & \\ & V = \left\{ \frac{45}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-4)& = & 6 \color{red}{+} (-5-2x) \\\Leftrightarrow & 5x-20& = &6-5-2x \\\Leftrightarrow & 5x \color{red}{-20} & = &1 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 5x+2x& = &1+20 \\\Leftrightarrow & 7x& = &21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{21}{ \color{red}{7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+1)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 2x+2& = &-5-15+x \\\Leftrightarrow & 2x \color{red}{+2} & = &-20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 2x-x& = &-20-2 \\\Leftrightarrow & x& = &-22 \\ & V = \left\{ -22 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-4)& = & -4 \color{red}{+} (-1-5x) \\\Leftrightarrow & -6x-8& = &-4-1-5x \\\Leftrightarrow & -6x \color{red}{-8} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -6x+5x& = &-5+8 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-5)& = & 3 \color{red}{-} (12+x) \\\Leftrightarrow & -6x-15& = &3-12-x \\\Leftrightarrow & -6x \color{red}{-15} & = &-9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -6x+x& = &-9+15 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+4)& = & 4 \color{red}{-} (-13+x) \\\Leftrightarrow & -6x+24& = &4+13-x \\\Leftrightarrow & -6x \color{red}{+24} & = &17 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -6x+x& = &17-24 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+6)& = & 8 \color{red}{+} (9+x) \\\Leftrightarrow & 30x+36& = &8+9+x \\\Leftrightarrow & 30x \color{red}{+36} & = &17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &17-36 \\\Leftrightarrow & 29x& = &-19 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-19}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x-2)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & 10x-4& = &-2+14-x \\\Leftrightarrow & 10x \color{red}{-4} & = &12 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 10x+x& = &12+4 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-3)& = & 13 \color{red}{-} (9+3x) \\\Leftrightarrow & 4x-6& = &13-9-3x \\\Leftrightarrow & 4x \color{red}{-6} & = &4 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 4x+3x& = &4+6 \\\Leftrightarrow & 7x& = &10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-4)& = & 9 \color{red}{+} (-15+x) \\\Leftrightarrow & 12x-8& = &9-15+x \\\Leftrightarrow & 12x \color{red}{-8} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &-6+8 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x-3)& = & 13 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-15& = &13+2-2x \\\Leftrightarrow & -15x \color{red}{-15} & = &15 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -15x+2x& = &15+15 \\\Leftrightarrow & -13x& = &30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+3)& = & -3 \color{red}{+} (8+x) \\\Leftrightarrow & 12x+12& = &-3+8+x \\\Leftrightarrow & 12x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &5-12 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)