Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x-6)& = & -4 \color{red}{-} (14-5x) \\\Leftrightarrow & 6x-18& = &-4-14+5x \\\Leftrightarrow & 6x \color{red}{-18} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 6x-5x& = &-18+18 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x+2)& = & -3 \color{red}{+} (13+x) \\\Leftrightarrow & -2x+4& = &-3+13+x \\\Leftrightarrow & -2x \color{red}{+4} & = &10 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -2x-x& = &10-4 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x-5)& = & 15 \color{red}{-} (8+x) \\\Leftrightarrow & 24x-20& = &15-8-x \\\Leftrightarrow & 24x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &7+20 \\\Leftrightarrow & 25x& = &27 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{27}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{27}{25} & & \\ & V = \left\{ \frac{27}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x+4)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & -8x+8& = &-4-12-x \\\Leftrightarrow & -8x \color{red}{+8} & = &-16 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -8x+x& = &-16-8 \\\Leftrightarrow & -7x& = &-24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x+3)& = & -9 \color{red}{+} (3-4x) \\\Leftrightarrow & 5x+15& = &-9+3-4x \\\Leftrightarrow & 5x \color{red}{+15} & = &-6 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 5x+4x& = &-6-15 \\\Leftrightarrow & 9x& = &-21 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-21}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+1)& = & 9 \color{red}{-} (-15+x) \\\Leftrightarrow & 2x+2& = &9+15-x \\\Leftrightarrow & 2x \color{red}{+2} & = &24 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 2x+x& = &24-2 \\\Leftrightarrow & 3x& = &22 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{22}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{22}{3} & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x+2)& = & -8 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+8& = &-8-12-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-20-8 \\\Leftrightarrow & -23x& = &-28 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-28}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{28}{23} & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-3)& = & 1 \color{red}{-} (-10-2x) \\\Leftrightarrow & 3x-9& = &1+10+2x \\\Leftrightarrow & 3x \color{red}{-9} & = &11 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & 3x-2x& = &11+9 \\\Leftrightarrow & x& = &20 \\ & V = \left\{ 20 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-2)& = & -8 \color{red}{-} (-2-5x) \\\Leftrightarrow & 36x-12& = &-8+2+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &-6+12 \\\Leftrightarrow & 31x& = &6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x-2)& = & 9 \color{red}{+} (4+4x) \\\Leftrightarrow & 5x-10& = &9+4+4x \\\Leftrightarrow & 5x \color{red}{-10} & = &13 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & 5x-4x& = &13+10 \\\Leftrightarrow & x& = &23 \\ & V = \left\{ 23 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+2)& = & -8 \color{red}{-} (5+x) \\\Leftrightarrow & 20x+8& = &-8-5-x \\\Leftrightarrow & 20x \color{red}{+8} & = &-13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &-13-8 \\\Leftrightarrow & 21x& = &-21 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-21}{ \color{red}{21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-5)& = & 1 \color{red}{+} (-3+x) \\\Leftrightarrow & -4x-20& = &1-3+x \\\Leftrightarrow & -4x \color{red}{-20} & = &-2 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -4x-x& = &-2+20 \\\Leftrightarrow & -5x& = &18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-18}{5} & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)