Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-x-2)=14+(-15+x)\)
2. \(2(5x-6)=1-(9-3x)\)
3. \(4(-4x+1)=-13-(13+3x)\)
4. \(5(5x-3)=15+(7-4x)\)
5. \(6(-5x-2)=-7+(10+x)\)
6. \(6(x-3)=6+(5+x)\)
7. \(6(2x+3)=2+(-9+x)\)
8. \(3(-6x-7)=-1+(-5-5x)\)
9. \(6(-2x+3)=-7-(1+x)\)
10. \(5(2x-3)=3+(-3-3x)\)
11. \(6(5x+4)=-9-(11+x)\)
12. \(2(-x+2)=-14+(10+3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-2)& = & 14 \color{red}{+} (-15+x) \\\Leftrightarrow & -2x-4& = &14-15+x \\\Leftrightarrow & -2x \color{red}{-4} & = &-1 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &-1+4 \\\Leftrightarrow & -3x& = &3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{3}{ \color{red}{-3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-6)& = & 1 \color{red}{-} (9-3x) \\\Leftrightarrow & 10x-12& = &1-9+3x \\\Leftrightarrow & 10x \color{red}{-12} & = &-8 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 10x-3x& = &-8+12 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x+1)& = & -13 \color{red}{-} (13+3x) \\\Leftrightarrow & -16x+4& = &-13-13-3x \\\Leftrightarrow & -16x \color{red}{+4} & = &-26 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -16x+3x& = &-26-4 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-3)& = & 15 \color{red}{+} (7-4x) \\\Leftrightarrow & 25x-15& = &15+7-4x \\\Leftrightarrow & 25x \color{red}{-15} & = &22 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 25x+4x& = &22+15 \\\Leftrightarrow & 29x& = &37 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{37}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{37}{29} & & \\ & V = \left\{ \frac{37}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x-2)& = & -7 \color{red}{+} (10+x) \\\Leftrightarrow & -30x-12& = &-7+10+x \\\Leftrightarrow & -30x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &3+12 \\\Leftrightarrow & -31x& = &15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-3)& = & 6 \color{red}{+} (5+x) \\\Leftrightarrow & 6x-18& = &6+5+x \\\Leftrightarrow & 6x \color{red}{-18} & = &11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 6x-x& = &11+18 \\\Leftrightarrow & 5x& = &29 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{29}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{29}{5} & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+3)& = & 2 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+18& = &2-9+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-7-18 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x-7)& = & -1 \color{red}{+} (-5-5x) \\\Leftrightarrow & -18x-21& = &-1-5-5x \\\Leftrightarrow & -18x \color{red}{-21} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -18x+5x& = &-6+21 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+3)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+18& = &-7-1-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-8-18 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-3)& = & 3 \color{red}{+} (-3-3x) \\\Leftrightarrow & 10x-15& = &3-3-3x \\\Leftrightarrow & 10x \color{red}{-15} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 10x+3x& = &0+15 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+4)& = & -9 \color{red}{-} (11+x) \\\Leftrightarrow & 30x+24& = &-9-11-x \\\Leftrightarrow & 30x \color{red}{+24} & = &-20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 30x+x& = &-20-24 \\\Leftrightarrow & 31x& = &-44 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-44}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-44}{31} & & \\ & V = \left\{ \frac{-44}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+2)& = & -14 \color{red}{+} (10+3x) \\\Leftrightarrow & -2x+4& = &-14+10+3x \\\Leftrightarrow & -2x \color{red}{+4} & = &-4 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -2x-3x& = &-4-4 \\\Leftrightarrow & -5x& = &-8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)