Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x+6)& = & -13 \color{red}{+} (2+x) \\\Leftrightarrow & 6x+12& = &-13+2+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-11-12 \\\Leftrightarrow & 5x& = &-23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+3)& = & -12 \color{red}{-} (1+x) \\\Leftrightarrow & -8x+6& = &-12-1-x \\\Leftrightarrow & -8x \color{red}{+6} & = &-13 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -8x+x& = &-13-6 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-5)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x-25& = &1+2-x \\\Leftrightarrow & 30x \color{red}{-25} & = &3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &3+25 \\\Leftrightarrow & 31x& = &28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-4)& = & 2 \color{red}{-} (-10-5x) \\\Leftrightarrow & -6x-8& = &2+10+5x \\\Leftrightarrow & -6x \color{red}{-8} & = &12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -6x-5x& = &12+8 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-5)& = & 4 \color{red}{-} (4+x) \\\Leftrightarrow & 36x-30& = &4-4-x \\\Leftrightarrow & 36x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 36x+x& = &0+30 \\\Leftrightarrow & 37x& = &30 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{30}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{30}{37} & & \\ & V = \left\{ \frac{30}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+7)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+42& = &-7-1-x \\\Leftrightarrow & -12x \color{red}{+42} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &-8-42 \\\Leftrightarrow & -11x& = &-50 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-50}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{50}{11} & & \\ & V = \left\{ \frac{50}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & 3 \color{red}{-} (-13+x) \\\Leftrightarrow & 8x-8& = &3+13-x \\\Leftrightarrow & 8x \color{red}{-8} & = &16 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &16+8 \\\Leftrightarrow & 9x& = &24 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{24}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-2)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & -36x-12& = &3-9-x \\\Leftrightarrow & -36x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -36x+x& = &-6+12 \\\Leftrightarrow & -35x& = &6 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{6}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x+1)& = & 14 \color{red}{+} (-9+2x) \\\Leftrightarrow & -9x+3& = &14-9+2x \\\Leftrightarrow & -9x \color{red}{+3} & = &5 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -9x-2x& = &5-3 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x-1)& = & 2 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x-5& = &2-4-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &-2+5 \\\Leftrightarrow & 17x& = &3 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{3}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+2)& = & 10 \color{red}{-} (9+x) \\\Leftrightarrow & 12x+6& = &10-9-x \\\Leftrightarrow & 12x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &1-6 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-5)& = & -10 \color{red}{-} (15+3x) \\\Leftrightarrow & 20x-25& = &-10-15-3x \\\Leftrightarrow & 20x \color{red}{-25} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 20x+3x& = &-25+25 \\\Leftrightarrow & 23x& = &0 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{0}{ \color{red}{23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)