Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+1)& = & 14 \color{red}{-} (-13+x) \\\Leftrightarrow & 8x+2& = &14+13-x \\\Leftrightarrow & 8x \color{red}{+2} & = &27 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 8x+x& = &27-2 \\\Leftrightarrow & 9x& = &25 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{25}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{25}{9} & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-2)& = & 8 \color{red}{-} (15+x) \\\Leftrightarrow & -24x-8& = &8-15-x \\\Leftrightarrow & -24x \color{red}{-8} & = &-7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &-7+8 \\\Leftrightarrow & -23x& = &1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+3)& = & 4 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x+6& = &4-11+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-7-6 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+2)& = & 8 \color{red}{+} (-8+x) \\\Leftrightarrow & -36x+12& = &8-8+x \\\Leftrightarrow & -36x \color{red}{+12} & = &0 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -36x-x& = &0-12 \\\Leftrightarrow & -37x& = &-12 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-12}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{12}{37} & & \\ & V = \left\{ \frac{12}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-1)& = & 2 \color{red}{-} (1-2x) \\\Leftrightarrow & 15x-3& = &2-1+2x \\\Leftrightarrow & 15x \color{red}{-3} & = &1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 15x-2x& = &1+3 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+4)& = & 3 \color{red}{+} (-1-2x) \\\Leftrightarrow & -15x+20& = &3-1-2x \\\Leftrightarrow & -15x \color{red}{+20} & = &2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -15x+2x& = &2-20 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x+3)& = & 9 \color{red}{+} (11+x) \\\Leftrightarrow & 20x+12& = &9+11+x \\\Leftrightarrow & 20x \color{red}{+12} & = &20 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 20x-x& = &20-12 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-1)& = & 13 \color{red}{+} (5+3x) \\\Leftrightarrow & 20x-4& = &13+5+3x \\\Leftrightarrow & 20x \color{red}{-4} & = &18 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 20x-3x& = &18+4 \\\Leftrightarrow & 17x& = &22 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{22}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{22}{17} & & \\ & V = \left\{ \frac{22}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-6)& = & 1 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-12& = &1+3+x \\\Leftrightarrow & 12x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &4+12 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-3)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-6& = &-8+14-x \\\Leftrightarrow & 12x \color{red}{-6} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &6+6 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-5)& = & -7 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-30& = &-7-15-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-22+30 \\\Leftrightarrow & 31x& = &8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{8}{31} & & \\ & V = \left\{ \frac{8}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+3)& = & -11 \color{red}{+} (11+x) \\\Leftrightarrow & 18x+18& = &-11+11+x \\\Leftrightarrow & 18x \color{red}{+18} & = &0 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &0-18 \\\Leftrightarrow & 17x& = &-18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-18}{17} & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)