Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+7)& = & 14 \color{red}{+} (-11-2x) \\\Leftrightarrow & -15x+35& = &14-11-2x \\\Leftrightarrow & -15x \color{red}{+35} & = &3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -15x+2x& = &3-35 \\\Leftrightarrow & -13x& = &-32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x-2)& = & -3 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-4& = &-3+1-x \\\Leftrightarrow & -12x \color{red}{-4} & = &-2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &-2+4 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-2)& = & 9 \color{red}{-} (15+3x) \\\Leftrightarrow & 5x-10& = &9-15-3x \\\Leftrightarrow & 5x \color{red}{-10} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 5x+3x& = &-6+10 \\\Leftrightarrow & 8x& = &4 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{4}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+1)& = & -5 \color{red}{+} (1+x) \\\Leftrightarrow & -24x+6& = &-5+1+x \\\Leftrightarrow & -24x \color{red}{+6} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -24x-x& = &-4-6 \\\Leftrightarrow & -25x& = &-10 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-10}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+1)& = & 6 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x+6& = &6+7+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &13-6 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-3)& = & 4 \color{red}{+} (3+x) \\\Leftrightarrow & -6x-18& = &4+3+x \\\Leftrightarrow & -6x \color{red}{-18} & = &7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &7+18 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x-1)& = & -8 \color{red}{-} (-3-5x) \\\Leftrightarrow & -6x-3& = &-8+3+5x \\\Leftrightarrow & -6x \color{red}{-3} & = &-5 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -6x-5x& = &-5+3 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-5)& = & 9 \color{red}{+} (-7+3x) \\\Leftrightarrow & -4x-20& = &9-7+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &2+20 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x-4)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & -6x-12& = &-3-3-x \\\Leftrightarrow & -6x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &-6+12 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-2)& = & -2 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x-8& = &-2+8+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &6 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &6+8 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+2)& = & 1 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x+8& = &1+4-x \\\Leftrightarrow & 20x \color{red}{+8} & = &5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &5-8 \\\Leftrightarrow & 21x& = &-3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x+4)& = & 12 \color{red}{+} (11+x) \\\Leftrightarrow & -6x+12& = &12+11+x \\\Leftrightarrow & -6x \color{red}{+12} & = &23 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &23-12 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)