Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-1)& = & 5 \color{red}{+} (11-5x) \\\Leftrightarrow & -6x-3& = &5+11-5x \\\Leftrightarrow & -6x \color{red}{-3} & = &16 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -6x+5x& = &16+3 \\\Leftrightarrow & -x& = &19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{19}{ \color{red}{-1} } \\\Leftrightarrow & x = -19 & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+7)& = & -15 \color{red}{-} (15+x) \\\Leftrightarrow & 30x+35& = &-15-15-x \\\Leftrightarrow & 30x \color{red}{+35} & = &-30 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-30 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &-30-35 \\\Leftrightarrow & 31x& = &-65 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-65}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-65}{31} & & \\ & V = \left\{ \frac{-65}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x-1)& = & -5 \color{red}{-} (-4-5x) \\\Leftrightarrow & -6x-6& = &-5+4+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &-1+6 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x+1)& = & 12 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x+6& = &12+2-x \\\Leftrightarrow & 30x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 30x+x& = &14-6 \\\Leftrightarrow & 31x& = &8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{8}{31} & & \\ & V = \left\{ \frac{8}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+7)& = & 15 \color{red}{+} (15-5x) \\\Leftrightarrow & -8x+28& = &15+15-5x \\\Leftrightarrow & -8x \color{red}{+28} & = &30 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &30 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & -8x+5x& = &30-28 \\\Leftrightarrow & -3x& = &2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+2)& = & -10 \color{red}{-} (-4+2x) \\\Leftrightarrow & 15x+10& = &-10+4-2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-6 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 15x+2x& = &-6-10 \\\Leftrightarrow & 17x& = &-16 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-16}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-16}{17} & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x-7)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & 6x-21& = &10-8-x \\\Leftrightarrow & 6x \color{red}{-21} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 6x+x& = &2+21 \\\Leftrightarrow & 7x& = &23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+7)& = & -4 \color{red}{-} (5-5x) \\\Leftrightarrow & -6x+21& = &-4-5+5x \\\Leftrightarrow & -6x \color{red}{+21} & = &-9 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -6x-5x& = &-9-21 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+2)& = & 3 \color{red}{-} (3+x) \\\Leftrightarrow & -10x+10& = &3-3-x \\\Leftrightarrow & -10x \color{red}{+10} & = &0 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -10x+x& = &0-10 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-7)& = & -1 \color{red}{-} (15-5x) \\\Leftrightarrow & -3x-21& = &-1-15+5x \\\Leftrightarrow & -3x \color{red}{-21} & = &-16 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -3x-5x& = &-16+21 \\\Leftrightarrow & -8x& = &5 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{5}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-5}{8} & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-2)& = & 15 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x-12& = &15+14-x \\\Leftrightarrow & 24x \color{red}{-12} & = &29 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &29+12 \\\Leftrightarrow & 25x& = &41 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{41}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{41}{25} & & \\ & V = \left\{ \frac{41}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+2)& = & 12 \color{red}{-} (6+x) \\\Leftrightarrow & 6x+6& = &12-6-x \\\Leftrightarrow & 6x \color{red}{+6} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &6-6 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)