Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+3)& = & 5 \color{red}{+} (-4-5x) \\\Leftrightarrow & -36x+18& = &5-4-5x \\\Leftrightarrow & -36x \color{red}{+18} & = &1 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -36x+5x& = &1-18 \\\Leftrightarrow & -31x& = &-17 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-17}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-6)& = & -6 \color{red}{-} (12-3x) \\\Leftrightarrow & -4x-24& = &-6-12+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &-18 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &-18+24 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-5)& = & -11 \color{red}{-} (3-2x) \\\Leftrightarrow & 25x-25& = &-11-3+2x \\\Leftrightarrow & 25x \color{red}{-25} & = &-14 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & 25x-2x& = &-14+25 \\\Leftrightarrow & 23x& = &11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-6)& = & -4 \color{red}{+} (-13+3x) \\\Leftrightarrow & -2x-12& = &-4-13+3x \\\Leftrightarrow & -2x \color{red}{-12} & = &-17 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -2x-3x& = &-17+12 \\\Leftrightarrow & -5x& = &-5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-5}{ \color{red}{-5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-1)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x-4& = &13+12-x \\\Leftrightarrow & 24x \color{red}{-4} & = &25 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &25+4 \\\Leftrightarrow & 25x& = &29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-1)& = & 13 \color{red}{-} (-3+x) \\\Leftrightarrow & 15x-3& = &13+3-x \\\Leftrightarrow & 15x \color{red}{-3} & = &16 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 15x+x& = &16+3 \\\Leftrightarrow & 16x& = &19 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{19}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{19}{16} & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-7)& = & -2 \color{red}{+} (5+x) \\\Leftrightarrow & 20x-28& = &-2+5+x \\\Leftrightarrow & 20x \color{red}{-28} & = &3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 20x-x& = &3+28 \\\Leftrightarrow & 19x& = &31 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{31}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{31}{19} & & \\ & V = \left\{ \frac{31}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-7)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & 2x-14& = &13+14+x \\\Leftrightarrow & 2x \color{red}{-14} & = &27 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 2x-x& = &27+14 \\\Leftrightarrow & x& = &41 \\ & V = \left\{ 41 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+4)& = & -6 \color{red}{-} (2-4x) \\\Leftrightarrow & -5x+20& = &-6-2+4x \\\Leftrightarrow & -5x \color{red}{+20} & = &-8 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -5x-4x& = &-8-20 \\\Leftrightarrow & -9x& = &-28 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-28}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{28}{9} & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-1)& = & 2 \color{red}{-} (6+4x) \\\Leftrightarrow & -9x-3& = &2-6-4x \\\Leftrightarrow & -9x \color{red}{-3} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & -9x+4x& = &-4+3 \\\Leftrightarrow & -5x& = &-1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-6)& = & -4 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x-30& = &-4+2-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-2+30 \\\Leftrightarrow & 31x& = &28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+3)& = & 9 \color{red}{+} (-13+x) \\\Leftrightarrow & 18x+9& = &9-13+x \\\Leftrightarrow & 18x \color{red}{+9} & = &-4 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 18x-x& = &-4-9 \\\Leftrightarrow & 17x& = &-13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)