Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+7)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & -6x+42& = &-11-10+x \\\Leftrightarrow & -6x \color{red}{+42} & = &-21 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -6x-x& = &-21-42 \\\Leftrightarrow & -7x& = &-63 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-63}{ \color{red}{-7} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x+3)& = & -2 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x+12& = &-2+5-x \\\Leftrightarrow & -24x \color{red}{+12} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &3-12 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-4)& = & -14 \color{red}{-} (-14-2x) \\\Leftrightarrow & 15x-20& = &-14+14+2x \\\Leftrightarrow & 15x \color{red}{-20} & = &0 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & 15x-2x& = &0+20 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-1)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x-3& = &10+5-x \\\Leftrightarrow & -12x \color{red}{-3} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &15+3 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-7)& = & 14 \color{red}{-} (-8+x) \\\Leftrightarrow & 30x-42& = &14+8-x \\\Leftrightarrow & 30x \color{red}{-42} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 30x+x& = &22+42 \\\Leftrightarrow & 31x& = &64 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{64}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{64}{31} & & \\ & V = \left\{ \frac{64}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-6)& = & 1 \color{red}{+} (4-4x) \\\Leftrightarrow & -9x-18& = &1+4-4x \\\Leftrightarrow & -9x \color{red}{-18} & = &5 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & -9x+4x& = &5+18 \\\Leftrightarrow & -5x& = &23 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{23}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x-2)& = & 11 \color{red}{+} (10-5x) \\\Leftrightarrow & -6x-12& = &11+10-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &21 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &21+12 \\\Leftrightarrow & -x& = &33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{33}{ \color{red}{-1} } \\\Leftrightarrow & x = -33 & & \\ & V = \left\{ -33 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-2)& = & 9 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-12& = &9-14+x \\\Leftrightarrow & -24x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &-5+12 \\\Leftrightarrow & -25x& = &7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-7)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & 2x-14& = &-9-1-x \\\Leftrightarrow & 2x \color{red}{-14} & = &-10 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 2x+x& = &-10+14 \\\Leftrightarrow & 3x& = &4 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{4}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-7)& = & 9 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x-21& = &9+10-x \\\Leftrightarrow & -12x \color{red}{-21} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -12x+x& = &19+21 \\\Leftrightarrow & -11x& = &40 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{40}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-2)& = & -8 \color{red}{+} (10+2x) \\\Leftrightarrow & 5x-10& = &-8+10+2x \\\Leftrightarrow & 5x \color{red}{-10} & = &2 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 5x-2x& = &2+10 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+1)& = & -1 \color{red}{-} (12-5x) \\\Leftrightarrow & 6x+2& = &-1-12+5x \\\Leftrightarrow & 6x \color{red}{+2} & = &-13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 6x-5x& = &-13-2 \\\Leftrightarrow & x& = &-15 \\ & V = \left\{ -15 \right\} & \\\end{align}\)