Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-2)& = & 1 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-12& = &1-5-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-4+12 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+7)& = & -1 \color{red}{+} (15-2x) \\\Leftrightarrow & -25x+35& = &-1+15-2x \\\Leftrightarrow & -25x \color{red}{+35} & = &14 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -25x+2x& = &14-35 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+1)& = & 14 \color{red}{+} (-15+4x) \\\Leftrightarrow & 25x+5& = &14-15+4x \\\Leftrightarrow & 25x \color{red}{+5} & = &-1 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 25x-4x& = &-1-5 \\\Leftrightarrow & 21x& = &-6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-7)& = & -14 \color{red}{+} (10-2x) \\\Leftrightarrow & 15x-35& = &-14+10-2x \\\Leftrightarrow & 15x \color{red}{-35} & = &-4 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 15x+2x& = &-4+35 \\\Leftrightarrow & 17x& = &31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{31}{17} & & \\ & V = \left\{ \frac{31}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-4)& = & -2 \color{red}{-} (6+x) \\\Leftrightarrow & 24x-16& = &-2-6-x \\\Leftrightarrow & 24x \color{red}{-16} & = &-8 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 24x+x& = &-8+16 \\\Leftrightarrow & 25x& = &8 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{8}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{8}{25} & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+7)& = & -1 \color{red}{-} (-10+x) \\\Leftrightarrow & 10x+14& = &-1+10-x \\\Leftrightarrow & 10x \color{red}{+14} & = &9 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 10x+x& = &9-14 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x+3)& = & 9 \color{red}{+} (-6+x) \\\Leftrightarrow & -24x+12& = &9-6+x \\\Leftrightarrow & -24x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &3-12 \\\Leftrightarrow & -25x& = &-9 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-9}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{9}{25} & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-2)& = & 11 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x-6& = &11+13-x \\\Leftrightarrow & 12x \color{red}{-6} & = &24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &24+6 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-6)& = & -13 \color{red}{+} (2+x) \\\Leftrightarrow & 24x-36& = &-13+2+x \\\Leftrightarrow & 24x \color{red}{-36} & = &-11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &-11+36 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x+4)& = & -2 \color{red}{+} (15+3x) \\\Leftrightarrow & -4x+16& = &-2+15+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &13-16 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-5)& = & -14 \color{red}{+} (-14-5x) \\\Leftrightarrow & -8x-10& = &-14-14-5x \\\Leftrightarrow & -8x \color{red}{-10} & = &-28 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &-28 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -8x+5x& = &-28+10 \\\Leftrightarrow & -3x& = &-18 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-18}{ \color{red}{-3} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+2)& = & -5 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+12& = &-5+13-x \\\Leftrightarrow & -12x \color{red}{+12} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &8-12 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)