Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+3)& = & 9 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+6& = &9+11+3x \\\Leftrightarrow & -4x \color{red}{+6} & = &20 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -4x-3x& = &20-6 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-1)& = & -8 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x-3& = &-8-14-2x \\\Leftrightarrow & 15x \color{red}{-3} & = &-22 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-22 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 15x+2x& = &-22+3 \\\Leftrightarrow & 17x& = &-19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-19}{17} & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-4)& = & 4 \color{red}{-} (10+x) \\\Leftrightarrow & 6x-8& = &4-10-x \\\Leftrightarrow & 6x \color{red}{-8} & = &-6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 6x+x& = &-6+8 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-6)& = & 6 \color{red}{-} (-11-5x) \\\Leftrightarrow & -8x-12& = &6+11+5x \\\Leftrightarrow & -8x \color{red}{-12} & = &17 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -8x-5x& = &17+12 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x+5)& = & -14 \color{red}{-} (-8+x) \\\Leftrightarrow & 30x+25& = &-14+8-x \\\Leftrightarrow & 30x \color{red}{+25} & = &-6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 30x+x& = &-6-25 \\\Leftrightarrow & 31x& = &-31 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-31}{ \color{red}{31} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x-1)& = & 5 \color{red}{+} (8+x) \\\Leftrightarrow & 36x-6& = &5+8+x \\\Leftrightarrow & 36x \color{red}{-6} & = &13 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 36x-x& = &13+6 \\\Leftrightarrow & 35x& = &19 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{19}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{19}{35} & & \\ & V = \left\{ \frac{19}{35} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x-6)& = & 3 \color{red}{+} (-2+x) \\\Leftrightarrow & -8x-24& = &3-2+x \\\Leftrightarrow & -8x \color{red}{-24} & = &1 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -8x-x& = &1+24 \\\Leftrightarrow & -9x& = &25 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{25}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-25}{9} & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+3)& = & -2 \color{red}{-} (-8-5x) \\\Leftrightarrow & 6x+18& = &-2+8+5x \\\Leftrightarrow & 6x \color{red}{+18} & = &6 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 6x-5x& = &6-18 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-1)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-2& = &-10-3-x \\\Leftrightarrow & 12x \color{red}{-2} & = &-13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &-13+2 \\\Leftrightarrow & 13x& = &-11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-2)& = & 9 \color{red}{+} (-1-2x) \\\Leftrightarrow & -9x-6& = &9-1-2x \\\Leftrightarrow & -9x \color{red}{-6} & = &8 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -9x+2x& = &8+6 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-2)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & -18x-6& = &-15+4+x \\\Leftrightarrow & -18x \color{red}{-6} & = &-11 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &-11+6 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+3)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x+18& = &-2+1-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-1-18 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)