Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-4)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & -2x-8& = &11+3+x \\\Leftrightarrow & -2x \color{red}{-8} & = &14 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -2x-x& = &14+8 \\\Leftrightarrow & -3x& = &22 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{22}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-22}{3} & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-6)& = & 11 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-24& = &11-11-x \\\Leftrightarrow & 12x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &0+24 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+3)& = & 1 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+6& = &1+12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &13-6 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-1)& = & -5 \color{red}{-} (-6-4x) \\\Leftrightarrow & 9x-3& = &-5+6+4x \\\Leftrightarrow & 9x \color{red}{-3} & = &1 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 9x-4x& = &1+3 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-5)& = & -1 \color{red}{+} (11+3x) \\\Leftrightarrow & -5x-25& = &-1+11+3x \\\Leftrightarrow & -5x \color{red}{-25} & = &10 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -5x-3x& = &10+25 \\\Leftrightarrow & -8x& = &35 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{35}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-35}{8} & & \\ & V = \left\{ \frac{-35}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+7)& = & 15 \color{red}{+} (-3+x) \\\Leftrightarrow & 8x+28& = &15-3+x \\\Leftrightarrow & 8x \color{red}{+28} & = &12 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 8x-x& = &12-28 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-1)& = & 10 \color{red}{+} (-6+3x) \\\Leftrightarrow & 4x-4& = &10-6+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &4+4 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-7)& = & 6 \color{red}{+} (-15+x) \\\Leftrightarrow & -24x-28& = &6-15+x \\\Leftrightarrow & -24x \color{red}{-28} & = &-9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &-9+28 \\\Leftrightarrow & -25x& = &19 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{19}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-19}{25} & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-7)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & -24x-42& = &3-5-x \\\Leftrightarrow & -24x \color{red}{-42} & = &-2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &-2+42 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-4)& = & -7 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-12& = &-7+14-x \\\Leftrightarrow & 12x \color{red}{-12} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &7+12 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x+5)& = & 9 \color{red}{-} (-9-5x) \\\Leftrightarrow & -6x+10& = &9+9+5x \\\Leftrightarrow & -6x \color{red}{+10} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -6x-5x& = &18-10 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+4)& = & -10 \color{red}{+} (9-3x) \\\Leftrightarrow & -10x+20& = &-10+9-3x \\\Leftrightarrow & -10x \color{red}{+20} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -10x+3x& = &-1-20 \\\Leftrightarrow & -7x& = &-21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-21}{ \color{red}{-7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)