Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-3)& = & 7 \color{red}{-} (-6-5x) \\\Leftrightarrow & 18x-18& = &7+6+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &13 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &13+18 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-4)& = & 5 \color{red}{-} (3-4x) \\\Leftrightarrow & -5x-20& = &5-3+4x \\\Leftrightarrow & -5x \color{red}{-20} & = &2 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -5x-4x& = &2+20 \\\Leftrightarrow & -9x& = &22 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{22}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+4)& = & 13 \color{red}{+} (15+x) \\\Leftrightarrow & -15x+20& = &13+15+x \\\Leftrightarrow & -15x \color{red}{+20} & = &28 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -15x-x& = &28-20 \\\Leftrightarrow & -16x& = &8 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{8}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x+1)& = & -8 \color{red}{+} (-1-3x) \\\Leftrightarrow & -4x+2& = &-8-1-3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -4x+3x& = &-9-2 \\\Leftrightarrow & -x& = &-11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-11}{ \color{red}{-1} } \\\Leftrightarrow & x = 11 & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x-5)& = & -14 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-20& = &-14-8-x \\\Leftrightarrow & -12x \color{red}{-20} & = &-22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -12x+x& = &-22+20 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-3)& = & 4 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-18& = &4-7-x \\\Leftrightarrow & -24x \color{red}{-18} & = &-3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -24x+x& = &-3+18 \\\Leftrightarrow & -23x& = &15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-5)& = & 15 \color{red}{-} (9+x) \\\Leftrightarrow & 24x-20& = &15-9-x \\\Leftrightarrow & 24x \color{red}{-20} & = &6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &6+20 \\\Leftrightarrow & 25x& = &26 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{26}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+1)& = & -6 \color{red}{-} (11-3x) \\\Leftrightarrow & -10x+2& = &-6-11+3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-17 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -10x-3x& = &-17-2 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+4)& = & -1 \color{red}{-} (-15-5x) \\\Leftrightarrow & -18x+12& = &-1+15+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &14 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &14-12 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+2)& = & -14 \color{red}{+} (-13+x) \\\Leftrightarrow & 36x+12& = &-14-13+x \\\Leftrightarrow & 36x \color{red}{+12} & = &-27 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 36x-x& = &-27-12 \\\Leftrightarrow & 35x& = &-39 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-39}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-39}{35} & & \\ & V = \left\{ \frac{-39}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+3)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & 2x+6& = &-3-6+x \\\Leftrightarrow & 2x \color{red}{+6} & = &-9 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 2x-x& = &-9-6 \\\Leftrightarrow & x& = &-15 \\ & V = \left\{ -15 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+7)& = & 12 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x+35& = &12-6-3x \\\Leftrightarrow & 10x \color{red}{+35} & = &6 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 10x+3x& = &6-35 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)