Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(2x-1)=-3+(2+5x)\)
2. \(2(6x-4)=-12-(-11+5x)\)
3. \(2(x+1)=-1-(8+3x)\)
4. \(3(5x+2)=6-(-2+4x)\)
5. \(6(5x-2)=11+(14+29x)\)
6. \(2(-2x-6)=13-(-2+5x)\)
7. \(4(-3x+5)=-12+(-6+5x)\)
8. \(6(5x+5)=-7+(-6+29x)\)
9. \(5(-x-6)=3-(9+x)\)
10. \(2(-x-6)=-2-(2+5x)\)
11. \(5(3x+6)=-1+(-2+x)\)
12. \(2(-5x+1)=-2-(-10-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-1)& = & -3 \color{red}{+} (2+5x) \\\Leftrightarrow & 8x-4& = &-3+2+5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 8x-5x& = &-1+4 \\\Leftrightarrow & 3x& = &3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{3}{ \color{red}{3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x-4)& = & -12 \color{red}{-} (-11+5x) \\\Leftrightarrow & 12x-8& = &-12+11-5x \\\Leftrightarrow & 12x \color{red}{-8} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 12x+5x& = &-1+8 \\\Leftrightarrow & 17x& = &7 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{7}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+1)& = & -1 \color{red}{-} (8+3x) \\\Leftrightarrow & 2x+2& = &-1-8-3x \\\Leftrightarrow & 2x \color{red}{+2} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 2x+3x& = &-9-2 \\\Leftrightarrow & 5x& = &-11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+2)& = & 6 \color{red}{-} (-2+4x) \\\Leftrightarrow & 15x+6& = &6+2-4x \\\Leftrightarrow & 15x \color{red}{+6} & = &8 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 15x+4x& = &8-6 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-2)& = & 11 \color{red}{+} (14+29x) \\\Leftrightarrow & 30x-12& = &11+14+29x \\\Leftrightarrow & 30x \color{red}{-12} & = &25 \color{red}{+29x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-29x} & = &25 \color{red}{+29x} \color{blue}{-29x} \color{blue}{+12} \\\Leftrightarrow & 30x-29x& = &25+12 \\\Leftrightarrow & x& = &37 \\ & V = \left\{ 37 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x-6)& = & 13 \color{red}{-} (-2+5x) \\\Leftrightarrow & -4x-12& = &13+2-5x \\\Leftrightarrow & -4x \color{red}{-12} & = &15 \color{red}{-5x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -4x+5x& = &15+12 \\\Leftrightarrow & x& = &27 \\ & V = \left\{ 27 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x+5)& = & -12 \color{red}{+} (-6+5x) \\\Leftrightarrow & -12x+20& = &-12-6+5x \\\Leftrightarrow & -12x \color{red}{+20} & = &-18 \color{red}{+5x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & -12x-5x& = &-18-20 \\\Leftrightarrow & -17x& = &-38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{38}{17} & & \\ & V = \left\{ \frac{38}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+5)& = & -7 \color{red}{+} (-6+29x) \\\Leftrightarrow & 30x+30& = &-7-6+29x \\\Leftrightarrow & 30x \color{red}{+30} & = &-13 \color{red}{+29x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-29x} & = &-13 \color{red}{+29x} \color{blue}{-29x} \color{blue}{-30} \\\Leftrightarrow & 30x-29x& = &-13-30 \\\Leftrightarrow & x& = &-43 \\ & V = \left\{ -43 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-6)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & -5x-30& = &3-9-x \\\Leftrightarrow & -5x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -5x+x& = &-6+30 \\\Leftrightarrow & -4x& = &24 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{24}{ \color{red}{-4} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x-6)& = & -2 \color{red}{-} (2+5x) \\\Leftrightarrow & -2x-12& = &-2-2-5x \\\Leftrightarrow & -2x \color{red}{-12} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -2x+5x& = &-4+12 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+6)& = & -1 \color{red}{+} (-2+x) \\\Leftrightarrow & 15x+30& = &-1-2+x \\\Leftrightarrow & 15x \color{red}{+30} & = &-3 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 15x-x& = &-3-30 \\\Leftrightarrow & 14x& = &-33 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-33}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-33}{14} & & \\ & V = \left\{ \frac{-33}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+1)& = & -2 \color{red}{-} (-10-3x) \\\Leftrightarrow & -10x+2& = &-2+10+3x \\\Leftrightarrow & -10x \color{red}{+2} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -10x-3x& = &8-2 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)