Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-1)& = & -2 \color{red}{+} (9+x) \\\Leftrightarrow & -2x-2& = &-2+9+x \\\Leftrightarrow & -2x \color{red}{-2} & = &7 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -2x-x& = &7+2 \\\Leftrightarrow & -3x& = &9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{9}{ \color{red}{-3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-1)& = & 7 \color{red}{-} (-8-4x) \\\Leftrightarrow & 25x-5& = &7+8+4x \\\Leftrightarrow & 25x \color{red}{-5} & = &15 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & 25x-4x& = &15+5 \\\Leftrightarrow & 21x& = &20 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{20}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-1)& = & 4 \color{red}{+} (9+3x) \\\Leftrightarrow & -10x-2& = &4+9+3x \\\Leftrightarrow & -10x \color{red}{-2} & = &13 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & -10x-3x& = &13+2 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+7)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & 2x+14& = &-8+14-x \\\Leftrightarrow & 2x \color{red}{+14} & = &6 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &6-14 \\\Leftrightarrow & 3x& = &-8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-1)& = & -7 \color{red}{-} (4+x) \\\Leftrightarrow & 24x-6& = &-7-4-x \\\Leftrightarrow & 24x \color{red}{-6} & = &-11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &-11+6 \\\Leftrightarrow & 25x& = &-5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x+2)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & -18x+6& = &1+2-x \\\Leftrightarrow & -18x \color{red}{+6} & = &3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -18x+x& = &3-6 \\\Leftrightarrow & -17x& = &-3 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-3}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-2)& = & 8 \color{red}{-} (-15-5x) \\\Leftrightarrow & 3x-6& = &8+15+5x \\\Leftrightarrow & 3x \color{red}{-6} & = &23 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 3x-5x& = &23+6 \\\Leftrightarrow & -2x& = &29 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{29}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-29}{2} & & \\ & V = \left\{ \frac{-29}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (3x+1)& = & 8 \color{red}{-} (-2+x) \\\Leftrightarrow & 18x+6& = &8+2-x \\\Leftrightarrow & 18x \color{red}{+6} & = &10 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &10-6 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+6)& = & 15 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x+36& = &15+2-x \\\Leftrightarrow & 30x \color{red}{+36} & = &17 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &17-36 \\\Leftrightarrow & 31x& = &-19 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-19}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-19}{31} & & \\ & V = \left\{ \frac{-19}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+4)& = & -12 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x+20& = &-12+12-x \\\Leftrightarrow & 30x \color{red}{+20} & = &0 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &0-20 \\\Leftrightarrow & 31x& = &-20 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-20}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-20}{31} & & \\ & V = \left\{ \frac{-20}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+3)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x+12& = &-7-1+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-8-12 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x-6)& = & 4 \color{red}{+} (9+x) \\\Leftrightarrow & -20x-24& = &4+9+x \\\Leftrightarrow & -20x \color{red}{-24} & = &13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &13+24 \\\Leftrightarrow & -21x& = &37 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{37}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)