Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x+2)& = & -9 \color{red}{-} (11+x) \\\Leftrightarrow & 36x+12& = &-9-11-x \\\Leftrightarrow & 36x \color{red}{+12} & = &-20 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 36x+x& = &-20-12 \\\Leftrightarrow & 37x& = &-32 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-32}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-32}{37} & & \\ & V = \left\{ \frac{-32}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+3)& = & -6 \color{red}{-} (-13-4x) \\\Leftrightarrow & -9x+9& = &-6+13+4x \\\Leftrightarrow & -9x \color{red}{+9} & = &7 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & -9x-4x& = &7-9 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+4)& = & 3 \color{red}{+} (-13+x) \\\Leftrightarrow & 30x+24& = &3-13+x \\\Leftrightarrow & 30x \color{red}{+24} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &-10-24 \\\Leftrightarrow & 29x& = &-34 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-34}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-34}{29} & & \\ & V = \left\{ \frac{-34}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+1)& = & -3 \color{red}{-} (-12-5x) \\\Leftrightarrow & 3x+3& = &-3+12+5x \\\Leftrightarrow & 3x \color{red}{+3} & = &9 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 3x-5x& = &9-3 \\\Leftrightarrow & -2x& = &6 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{6}{ \color{red}{-2} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+2)& = & -7 \color{red}{-} (-3-5x) \\\Leftrightarrow & -18x+6& = &-7+3+5x \\\Leftrightarrow & -18x \color{red}{+6} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -18x-5x& = &-4-6 \\\Leftrightarrow & -23x& = &-10 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-10}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+7)& = & 2 \color{red}{-} (4-4x) \\\Leftrightarrow & 9x+21& = &2-4+4x \\\Leftrightarrow & 9x \color{red}{+21} & = &-2 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 9x-4x& = &-2-21 \\\Leftrightarrow & 5x& = &-23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x-6)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x-36& = &1+11-x \\\Leftrightarrow & 24x \color{red}{-36} & = &12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &12+36 \\\Leftrightarrow & 25x& = &48 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{48}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{48}{25} & & \\ & V = \left\{ \frac{48}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-1)& = & 15 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-6& = &15+3-x \\\Leftrightarrow & -12x \color{red}{-6} & = &18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &18+6 \\\Leftrightarrow & -11x& = &24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+3)& = & 9 \color{red}{-} (11-2x) \\\Leftrightarrow & -5x+15& = &9-11+2x \\\Leftrightarrow & -5x \color{red}{+15} & = &-2 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -5x-2x& = &-2-15 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x-3)& = & 1 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-18& = &1-11-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-10+18 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-6)& = & -8 \color{red}{-} (-6-2x) \\\Leftrightarrow & -9x-18& = &-8+6+2x \\\Leftrightarrow & -9x \color{red}{-18} & = &-2 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -9x-2x& = &-2+18 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+3)& = & -12 \color{red}{-} (15+x) \\\Leftrightarrow & 8x+6& = &-12-15-x \\\Leftrightarrow & 8x \color{red}{+6} & = &-27 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 8x+x& = &-27-6 \\\Leftrightarrow & 9x& = &-33 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-33}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)