Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+5)& = & 10 \color{red}{+} (2+x) \\\Leftrightarrow & 8x+10& = &10+2+x \\\Leftrightarrow & 8x \color{red}{+10} & = &12 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 8x-x& = &12-10 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+2)& = & 7 \color{red}{+} (3+x) \\\Leftrightarrow & 12x+8& = &7+3+x \\\Leftrightarrow & 12x \color{red}{+8} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &10-8 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-7)& = & -15 \color{red}{+} (-12+x) \\\Leftrightarrow & 30x-35& = &-15-12+x \\\Leftrightarrow & 30x \color{red}{-35} & = &-27 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &-27+35 \\\Leftrightarrow & 29x& = &8 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{8}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-6)& = & -9 \color{red}{+} (1+x) \\\Leftrightarrow & 12x-36& = &-9+1+x \\\Leftrightarrow & 12x \color{red}{-36} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 12x-x& = &-8+36 \\\Leftrightarrow & 11x& = &28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-7)& = & -11 \color{red}{-} (-15+4x) \\\Leftrightarrow & 3x-21& = &-11+15-4x \\\Leftrightarrow & 3x \color{red}{-21} & = &4 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 3x+4x& = &4+21 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x-2)& = & 2 \color{red}{-} (-2+x) \\\Leftrightarrow & 6x-6& = &2+2-x \\\Leftrightarrow & 6x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &4+6 \\\Leftrightarrow & 7x& = &10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-4)& = & 1 \color{red}{-} (8+4x) \\\Leftrightarrow & -15x-20& = &1-8-4x \\\Leftrightarrow & -15x \color{red}{-20} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -15x+4x& = &-7+20 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-7)& = & -2 \color{red}{+} (-9-2x) \\\Leftrightarrow & -9x-21& = &-2-9-2x \\\Leftrightarrow & -9x \color{red}{-21} & = &-11 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & -9x+2x& = &-11+21 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-4)& = & 2 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x-16& = &2-15+x \\\Leftrightarrow & -20x \color{red}{-16} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -20x-x& = &-13+16 \\\Leftrightarrow & -21x& = &3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x+5)& = & 7 \color{red}{+} (-1+x) \\\Leftrightarrow & -5x+25& = &7-1+x \\\Leftrightarrow & -5x \color{red}{+25} & = &6 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -5x-x& = &6-25 \\\Leftrightarrow & -6x& = &-19 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-19}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{19}{6} & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x-2)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & 3x-6& = &7-11+x \\\Leftrightarrow & 3x \color{red}{-6} & = &-4 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 3x-x& = &-4+6 \\\Leftrightarrow & 2x& = &2 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{2}{ \color{red}{2} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+2)& = & 6 \color{red}{+} (-12+3x) \\\Leftrightarrow & 4x+8& = &6-12+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &-6-8 \\\Leftrightarrow & x& = &-14 \\ & V = \left\{ -14 \right\} & \\\end{align}\)