Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-6)& = & -6 \color{red}{-} (-15+x) \\\Leftrightarrow & 2x-12& = &-6+15-x \\\Leftrightarrow & 2x \color{red}{-12} & = &9 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 2x+x& = &9+12 \\\Leftrightarrow & 3x& = &21 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{21}{ \color{red}{3} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+4)& = & -10 \color{red}{-} (-1+2x) \\\Leftrightarrow & 5x+20& = &-10+1-2x \\\Leftrightarrow & 5x \color{red}{+20} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 5x+2x& = &-9-20 \\\Leftrightarrow & 7x& = &-29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-29}{7} & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+5)& = & -15 \color{red}{+} (-7-3x) \\\Leftrightarrow & 10x+10& = &-15-7-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-22 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &-22-10 \\\Leftrightarrow & 13x& = &-32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+6)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & -30x+30& = &2+3+x \\\Leftrightarrow & -30x \color{red}{+30} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &5-30 \\\Leftrightarrow & -31x& = &-25 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-25}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{25}{31} & & \\ & V = \left\{ \frac{25}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x+6)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & -15x+18& = &-2+4+x \\\Leftrightarrow & -15x \color{red}{+18} & = &2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -15x-x& = &2-18 \\\Leftrightarrow & -16x& = &-16 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-16}{ \color{red}{-16} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-1)& = & -2 \color{red}{+} (-5-3x) \\\Leftrightarrow & 10x-2& = &-2-5-3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 10x+3x& = &-7+2 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+6)& = & 1 \color{red}{+} (-4+3x) \\\Leftrightarrow & -2x+12& = &1-4+3x \\\Leftrightarrow & -2x \color{red}{+12} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -2x-3x& = &-3-12 \\\Leftrightarrow & -5x& = &-15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-15}{ \color{red}{-5} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-4)& = & 2 \color{red}{+} (-8+x) \\\Leftrightarrow & 3x-12& = &2-8+x \\\Leftrightarrow & 3x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 3x-x& = &-6+12 \\\Leftrightarrow & 2x& = &6 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{6}{ \color{red}{2} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+1)& = & 1 \color{red}{+} (-4+x) \\\Leftrightarrow & 6x+3& = &1-4+x \\\Leftrightarrow & 6x \color{red}{+3} & = &-3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 6x-x& = &-3-3 \\\Leftrightarrow & 5x& = &-6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-2)& = & -1 \color{red}{-} (12+x) \\\Leftrightarrow & -3x-6& = &-1-12-x \\\Leftrightarrow & -3x \color{red}{-6} & = &-13 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -3x+x& = &-13+6 \\\Leftrightarrow & -2x& = &-7 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-7}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{7}{2} & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+1)& = & -12 \color{red}{+} (9+x) \\\Leftrightarrow & -24x+6& = &-12+9+x \\\Leftrightarrow & -24x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -24x-x& = &-3-6 \\\Leftrightarrow & -25x& = &-9 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-9}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{9}{25} & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x+5)& = & -2 \color{red}{-} (11-4x) \\\Leftrightarrow & -5x+25& = &-2-11+4x \\\Leftrightarrow & -5x \color{red}{+25} & = &-13 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & -5x-4x& = &-13-25 \\\Leftrightarrow & -9x& = &-38 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-38}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{38}{9} & & \\ & V = \left\{ \frac{38}{9} \right\} & \\\end{align}\)