Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+4)& = & 9 \color{red}{+} (5-5x) \\\Leftrightarrow & -18x+12& = &9+5-5x \\\Leftrightarrow & -18x \color{red}{+12} & = &14 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -18x+5x& = &14-12 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+4)& = & -11 \color{red}{+} (13+4x) \\\Leftrightarrow & -25x+20& = &-11+13+4x \\\Leftrightarrow & -25x \color{red}{+20} & = &2 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -25x-4x& = &2-20 \\\Leftrightarrow & -29x& = &-18 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-18}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+5)& = & -9 \color{red}{+} (11+3x) \\\Leftrightarrow & -4x+10& = &-9+11+3x \\\Leftrightarrow & -4x \color{red}{+10} & = &2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -4x-3x& = &2-10 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x+3)& = & -8 \color{red}{+} (-1+3x) \\\Leftrightarrow & -8x+12& = &-8-1+3x \\\Leftrightarrow & -8x \color{red}{+12} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -8x-3x& = &-9-12 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-4)& = & 12 \color{red}{+} (14+x) \\\Leftrightarrow & -18x-12& = &12+14+x \\\Leftrightarrow & -18x \color{red}{-12} & = &26 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &26+12 \\\Leftrightarrow & -19x& = &38 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{38}{ \color{red}{-19} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+7)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+21& = &6+9+x \\\Leftrightarrow & 12x \color{red}{+21} & = &15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 12x-x& = &15-21 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x+1)& = & 6 \color{red}{-} (-4+3x) \\\Leftrightarrow & -10x+2& = &6+4-3x \\\Leftrightarrow & -10x \color{red}{+2} & = &10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -10x+3x& = &10-2 \\\Leftrightarrow & -7x& = &8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+2)& = & 15 \color{red}{+} (-1+2x) \\\Leftrightarrow & -15x+6& = &15-1+2x \\\Leftrightarrow & -15x \color{red}{+6} & = &14 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -15x-2x& = &14-6 \\\Leftrightarrow & -17x& = &8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+2)& = & -7 \color{red}{-} (15+3x) \\\Leftrightarrow & -8x+8& = &-7-15-3x \\\Leftrightarrow & -8x \color{red}{+8} & = &-22 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -8x+3x& = &-22-8 \\\Leftrightarrow & -5x& = &-30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-30}{ \color{red}{-5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+7)& = & -12 \color{red}{+} (4+x) \\\Leftrightarrow & -30x+35& = &-12+4+x \\\Leftrightarrow & -30x \color{red}{+35} & = &-8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &-8-35 \\\Leftrightarrow & -31x& = &-43 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-43}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{43}{31} & & \\ & V = \left\{ \frac{43}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-3)& = & -6 \color{red}{-} (-6+3x) \\\Leftrightarrow & -16x-12& = &-6+6-3x \\\Leftrightarrow & -16x \color{red}{-12} & = &0 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -16x+3x& = &0+12 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-6)& = & 10 \color{red}{+} (15+3x) \\\Leftrightarrow & -8x-12& = &10+15+3x \\\Leftrightarrow & -8x \color{red}{-12} & = &25 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -8x-3x& = &25+12 \\\Leftrightarrow & -11x& = &37 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{37}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-37}{11} & & \\ & V = \left\{ \frac{-37}{11} \right\} & \\\end{align}\)