Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-5)& = & 9 \color{red}{+} (-14+3x) \\\Leftrightarrow & -10x-25& = &9-14+3x \\\Leftrightarrow & -10x \color{red}{-25} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -10x-3x& = &-5+25 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-5)& = & -8 \color{red}{+} (15-3x) \\\Leftrightarrow & -10x-10& = &-8+15-3x \\\Leftrightarrow & -10x \color{red}{-10} & = &7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -10x+3x& = &7+10 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+5)& = & -1 \color{red}{-} (-6+2x) \\\Leftrightarrow & 9x+15& = &-1+6-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &5 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &5-15 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-3)& = & 13 \color{red}{-} (2-5x) \\\Leftrightarrow & 16x-12& = &13-2+5x \\\Leftrightarrow & 16x \color{red}{-12} & = &11 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 16x-5x& = &11+12 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-5)& = & -6 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x-20& = &-6+13-x \\\Leftrightarrow & 12x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &7+20 \\\Leftrightarrow & 13x& = &27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x+6)& = & 14 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+18& = &14-5+x \\\Leftrightarrow & -12x \color{red}{+18} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &9-18 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x-1)& = & 8 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-3& = &8-8-x \\\Leftrightarrow & -12x \color{red}{-3} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &0+3 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x-5)& = & -1 \color{red}{-} (3-5x) \\\Leftrightarrow & 16x-20& = &-1-3+5x \\\Leftrightarrow & 16x \color{red}{-20} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 16x-5x& = &-4+20 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x-4)& = & -9 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x-12& = &-9+6-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-3+12 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+7)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & 36x+42& = &-9-2+x \\\Leftrightarrow & 36x \color{red}{+42} & = &-11 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 36x-x& = &-11-42 \\\Leftrightarrow & 35x& = &-53 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-53}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-53}{35} & & \\ & V = \left\{ \frac{-53}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+6)& = & -10 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x+24& = &-10+3-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-7-24 \\\Leftrightarrow & 25x& = &-31 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-31}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-7)& = & -10 \color{red}{+} (-2-3x) \\\Leftrightarrow & -10x-35& = &-10-2-3x \\\Leftrightarrow & -10x \color{red}{-35} & = &-12 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & -10x+3x& = &-12+35 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)