Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+1)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & 10x+2& = &-9+8-x \\\Leftrightarrow & 10x \color{red}{+2} & = &-1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 10x+x& = &-1-2 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-2)& = & -1 \color{red}{+} (-4+x) \\\Leftrightarrow & 3x-6& = &-1-4+x \\\Leftrightarrow & 3x \color{red}{-6} & = &-5 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 3x-x& = &-5+6 \\\Leftrightarrow & 2x& = &1 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{1}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-3)& = & 14 \color{red}{-} (3+x) \\\Leftrightarrow & -20x-12& = &14-3-x \\\Leftrightarrow & -20x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -20x+x& = &11+12 \\\Leftrightarrow & -19x& = &23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-1)& = & 10 \color{red}{+} (10-4x) \\\Leftrightarrow & 25x-5& = &10+10-4x \\\Leftrightarrow & 25x \color{red}{-5} & = &20 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & 25x+4x& = &20+5 \\\Leftrightarrow & 29x& = &25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-7)& = & -15 \color{red}{+} (2+2x) \\\Leftrightarrow & -25x-35& = &-15+2+2x \\\Leftrightarrow & -25x \color{red}{-35} & = &-13 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -25x-2x& = &-13+35 \\\Leftrightarrow & -27x& = &22 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{22}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-22}{27} & & \\ & V = \left\{ \frac{-22}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x-6)& = & -4 \color{red}{+} (7-5x) \\\Leftrightarrow & 6x-18& = &-4+7-5x \\\Leftrightarrow & 6x \color{red}{-18} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 6x+5x& = &3+18 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-4)& = & 11 \color{red}{-} (9+x) \\\Leftrightarrow & -8x-8& = &11-9-x \\\Leftrightarrow & -8x \color{red}{-8} & = &2 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &2+8 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x-2)& = & -5 \color{red}{-} (2+x) \\\Leftrightarrow & -15x-10& = &-5-2-x \\\Leftrightarrow & -15x \color{red}{-10} & = &-7 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -15x+x& = &-7+10 \\\Leftrightarrow & -14x& = &3 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{3}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-2)& = & 9 \color{red}{-} (13+x) \\\Leftrightarrow & 12x-12& = &9-13-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-4+12 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+5)& = & -2 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+20& = &-2-12-x \\\Leftrightarrow & -24x \color{red}{+20} & = &-14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &-14-20 \\\Leftrightarrow & -23x& = &-34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-7)& = & 9 \color{red}{+} (2+x) \\\Leftrightarrow & -24x-28& = &9+2+x \\\Leftrightarrow & -24x \color{red}{-28} & = &11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &11+28 \\\Leftrightarrow & -25x& = &39 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{39}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-39}{25} & & \\ & V = \left\{ \frac{-39}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-1)& = & 1 \color{red}{+} (1+x) \\\Leftrightarrow & 30x-6& = &1+1+x \\\Leftrightarrow & 30x \color{red}{-6} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &2+6 \\\Leftrightarrow & 29x& = &8 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{8}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)