Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+1)& = & -2 \color{red}{-} (4-5x) \\\Leftrightarrow & 8x+4& = &-2-4+5x \\\Leftrightarrow & 8x \color{red}{+4} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 8x-5x& = &-6-4 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+5)& = & 15 \color{red}{-} (15+x) \\\Leftrightarrow & 30x+25& = &15-15-x \\\Leftrightarrow & 30x \color{red}{+25} & = &0 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 30x+x& = &0-25 \\\Leftrightarrow & 31x& = &-25 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-25}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-25}{31} & & \\ & V = \left\{ \frac{-25}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-1)& = & -12 \color{red}{+} (-4-2x) \\\Leftrightarrow & 25x-5& = &-12-4-2x \\\Leftrightarrow & 25x \color{red}{-5} & = &-16 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 25x+2x& = &-16+5 \\\Leftrightarrow & 27x& = &-11 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{-11}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{-11}{27} & & \\ & V = \left\{ \frac{-11}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+4)& = & 2 \color{red}{-} (-6-3x) \\\Leftrightarrow & 10x+20& = &2+6+3x \\\Leftrightarrow & 10x \color{red}{+20} & = &8 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 10x-3x& = &8-20 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-7)& = & -14 \color{red}{+} (-2-5x) \\\Leftrightarrow & 8x-14& = &-14-2-5x \\\Leftrightarrow & 8x \color{red}{-14} & = &-16 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & 8x+5x& = &-16+14 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x+1)& = & -10 \color{red}{+} (7-5x) \\\Leftrightarrow & 16x+4& = &-10+7-5x \\\Leftrightarrow & 16x \color{red}{+4} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 16x+5x& = &-3-4 \\\Leftrightarrow & 21x& = &-7 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-7}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+1)& = & -13 \color{red}{-} (-2-5x) \\\Leftrightarrow & 8x+2& = &-13+2+5x \\\Leftrightarrow & 8x \color{red}{+2} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 8x-5x& = &-11-2 \\\Leftrightarrow & 3x& = &-13 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-13}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-2)& = & -8 \color{red}{-} (-3+x) \\\Leftrightarrow & 20x-10& = &-8+3-x \\\Leftrightarrow & 20x \color{red}{-10} & = &-5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 20x+x& = &-5+10 \\\Leftrightarrow & 21x& = &5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-3)& = & 1 \color{red}{+} (-4-5x) \\\Leftrightarrow & 16x-12& = &1-4-5x \\\Leftrightarrow & 16x \color{red}{-12} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 16x+5x& = &-3+12 \\\Leftrightarrow & 21x& = &9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x+3)& = & -3 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+18& = &-3-4-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-7-18 \\\Leftrightarrow & 13x& = &-25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-1)& = & -8 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x-6& = &-8-8+x \\\Leftrightarrow & 24x \color{red}{-6} & = &-16 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &-16+6 \\\Leftrightarrow & 23x& = &-10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-10}{23} & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-4)& = & 3 \color{red}{+} (9+3x) \\\Leftrightarrow & -20x-20& = &3+9+3x \\\Leftrightarrow & -20x \color{red}{-20} & = &12 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -20x-3x& = &12+20 \\\Leftrightarrow & -23x& = &32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-32}{23} & & \\ & V = \left\{ \frac{-32}{23} \right\} & \\\end{align}\)