Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-2)& = & 15 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-6& = &15-2+x \\\Leftrightarrow & -12x \color{red}{-6} & = &13 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &13+6 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-7)& = & -1 \color{red}{-} (-11+4x) \\\Leftrightarrow & 25x-35& = &-1+11-4x \\\Leftrightarrow & 25x \color{red}{-35} & = &10 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 25x+4x& = &10+35 \\\Leftrightarrow & 29x& = &45 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{45}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{45}{29} & & \\ & V = \left\{ \frac{45}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-4)& = & -5 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-8& = &-5+6+x \\\Leftrightarrow & -12x \color{red}{-8} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &1+8 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-6)& = & -11 \color{red}{-} (-3+x) \\\Leftrightarrow & -6x-36& = &-11+3-x \\\Leftrightarrow & -6x \color{red}{-36} & = &-8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -6x+x& = &-8+36 \\\Leftrightarrow & -5x& = &28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x+1)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & -30x+6& = &-10+9+x \\\Leftrightarrow & -30x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -30x-x& = &-1-6 \\\Leftrightarrow & -31x& = &-7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+2)& = & 1 \color{red}{-} (10+4x) \\\Leftrightarrow & -3x+6& = &1-10-4x \\\Leftrightarrow & -3x \color{red}{+6} & = &-9 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &-9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & -3x+4x& = &-9-6 \\\Leftrightarrow & x& = &-15 \\ & V = \left\{ -15 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x-4)& = & 15 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-12& = &15-5-x \\\Leftrightarrow & -12x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &10+12 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+7)& = & -9 \color{red}{-} (-14-3x) \\\Leftrightarrow & -10x+14& = &-9+14+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &5-14 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-4)& = & 10 \color{red}{+} (-12+x) \\\Leftrightarrow & -4x-16& = &10-12+x \\\Leftrightarrow & -4x \color{red}{-16} & = &-2 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &-2+16 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-1)& = & 12 \color{red}{-} (14+3x) \\\Leftrightarrow & -8x-4& = &12-14-3x \\\Leftrightarrow & -8x \color{red}{-4} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -8x+3x& = &-2+4 \\\Leftrightarrow & -5x& = &2 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{2}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-3)& = & -3 \color{red}{+} (4+x) \\\Leftrightarrow & 8x-12& = &-3+4+x \\\Leftrightarrow & 8x \color{red}{-12} & = &1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 8x-x& = &1+12 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-4)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & -30x-20& = &2+10+x \\\Leftrightarrow & -30x \color{red}{-20} & = &12 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &12+20 \\\Leftrightarrow & -31x& = &32 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{32}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-32}{31} & & \\ & V = \left\{ \frac{-32}{31} \right\} & \\\end{align}\)