Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-2)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & -15x-6& = &14+2-x \\\Leftrightarrow & -15x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -15x+x& = &16+6 \\\Leftrightarrow & -14x& = &22 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{22}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x-2)& = & -11 \color{red}{-} (-13+x) \\\Leftrightarrow & -30x-12& = &-11+13-x \\\Leftrightarrow & -30x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &2+12 \\\Leftrightarrow & -29x& = &14 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{14}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-14}{29} & & \\ & V = \left\{ \frac{-14}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-4)& = & -3 \color{red}{+} (-15+x) \\\Leftrightarrow & -4x-16& = &-3-15+x \\\Leftrightarrow & -4x \color{red}{-16} & = &-18 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &-18+16 \\\Leftrightarrow & -5x& = &-2 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-2}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+6)& = & -2 \color{red}{-} (8+x) \\\Leftrightarrow & 6x+36& = &-2-8-x \\\Leftrightarrow & 6x \color{red}{+36} & = &-10 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 6x+x& = &-10-36 \\\Leftrightarrow & 7x& = &-46 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-46}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-46}{7} & & \\ & V = \left\{ \frac{-46}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-7)& = & -14 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-28& = &-14-11-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-25 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-25+28 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-3)& = & 11 \color{red}{-} (-2-5x) \\\Leftrightarrow & -36x-18& = &11+2+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &13 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &13+18 \\\Leftrightarrow & -41x& = &31 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{31}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-31}{41} & & \\ & V = \left\{ \frac{-31}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+4)& = & 2 \color{red}{-} (9+x) \\\Leftrightarrow & 12x+8& = &2-9-x \\\Leftrightarrow & 12x \color{red}{+8} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &-7-8 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x-1)& = & 2 \color{red}{+} (-2-4x) \\\Leftrightarrow & -5x-5& = &2-2-4x \\\Leftrightarrow & -5x \color{red}{-5} & = &0 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & -5x+4x& = &0+5 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+7)& = & -4 \color{red}{-} (11+x) \\\Leftrightarrow & 2x+14& = &-4-11-x \\\Leftrightarrow & 2x \color{red}{+14} & = &-15 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &-15-14 \\\Leftrightarrow & 3x& = &-29 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-29}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-29}{3} & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-4)& = & -14 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x-24& = &-14-12-5x \\\Leftrightarrow & -6x \color{red}{-24} & = &-26 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-26 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -6x+5x& = &-26+24 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-4)& = & -11 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-8& = &-11-6+x \\\Leftrightarrow & 6x \color{red}{-8} & = &-17 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 6x-x& = &-17+8 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+2)& = & -1 \color{red}{+} (-14+x) \\\Leftrightarrow & -18x+12& = &-1-14+x \\\Leftrightarrow & -18x \color{red}{+12} & = &-15 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &-15-12 \\\Leftrightarrow & -19x& = &-27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{27}{19} & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)