Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+4)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & -18x+12& = &9+4-x \\\Leftrightarrow & -18x \color{red}{+12} & = &13 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -18x+x& = &13-12 \\\Leftrightarrow & -17x& = &1 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{1}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+7)& = & 7 \color{red}{-} (15+x) \\\Leftrightarrow & -5x+35& = &7-15-x \\\Leftrightarrow & -5x \color{red}{+35} & = &-8 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -5x+x& = &-8-35 \\\Leftrightarrow & -4x& = &-43 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-43}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{43}{4} & & \\ & V = \left\{ \frac{43}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-1)& = & 14 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-3& = &14+12-x \\\Leftrightarrow & 12x \color{red}{-3} & = &26 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &26+3 \\\Leftrightarrow & 13x& = &29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-5)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & -6x-10& = &-11-15-x \\\Leftrightarrow & -6x \color{red}{-10} & = &-26 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -6x+x& = &-26+10 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-1)& = & 8 \color{red}{+} (-12+x) \\\Leftrightarrow & 36x-6& = &8-12+x \\\Leftrightarrow & 36x \color{red}{-6} & = &-4 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 36x-x& = &-4+6 \\\Leftrightarrow & 35x& = &2 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{2}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x+2)& = & 15 \color{red}{+} (-5+x) \\\Leftrightarrow & -24x+12& = &15-5+x \\\Leftrightarrow & -24x \color{red}{+12} & = &10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &10-12 \\\Leftrightarrow & -25x& = &-2 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-2}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+2)& = & 3 \color{red}{-} (14-5x) \\\Leftrightarrow & 6x+4& = &3-14+5x \\\Leftrightarrow & 6x \color{red}{+4} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 6x-5x& = &-11-4 \\\Leftrightarrow & x& = &-15 \\ & V = \left\{ -15 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-3)& = & 14 \color{red}{-} (-1-4x) \\\Leftrightarrow & 5x-15& = &14+1+4x \\\Leftrightarrow & 5x \color{red}{-15} & = &15 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 5x-4x& = &15+15 \\\Leftrightarrow & x& = &30 \\ & V = \left\{ 30 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-6)& = & 3 \color{red}{-} (-6+x) \\\Leftrightarrow & -36x-36& = &3+6-x \\\Leftrightarrow & -36x \color{red}{-36} & = &9 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -36x+x& = &9+36 \\\Leftrightarrow & -35x& = &45 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{45}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-5)& = & 10 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x-20& = &10-11+x \\\Leftrightarrow & 12x \color{red}{-20} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 12x-x& = &-1+20 \\\Leftrightarrow & 11x& = &19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-3)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & -36x-18& = &14+6-x \\\Leftrightarrow & -36x \color{red}{-18} & = &20 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -36x+x& = &20+18 \\\Leftrightarrow & -35x& = &38 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{38}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-38}{35} & & \\ & V = \left\{ \frac{-38}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x+3)& = & 6 \color{red}{-} (12-5x) \\\Leftrightarrow & -6x+6& = &6-12+5x \\\Leftrightarrow & -6x \color{red}{+6} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -6x-5x& = &-6-6 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)