Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+5)& = & 14 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+30& = &14+5+x \\\Leftrightarrow & 12x \color{red}{+30} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 12x-x& = &19-30 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x+3)& = & 5 \color{red}{-} (15-3x) \\\Leftrightarrow & 4x+12& = &5-15+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &-10-12 \\\Leftrightarrow & x& = &-22 \\ & V = \left\{ -22 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+2)& = & 15 \color{red}{-} (-14-2x) \\\Leftrightarrow & -15x+10& = &15+14+2x \\\Leftrightarrow & -15x \color{red}{+10} & = &29 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &29 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & -15x-2x& = &29-10 \\\Leftrightarrow & -17x& = &19 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{19}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-19}{17} & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-2)& = & -7 \color{red}{+} (-2+4x) \\\Leftrightarrow & 15x-10& = &-7-2+4x \\\Leftrightarrow & 15x \color{red}{-10} & = &-9 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & 15x-4x& = &-9+10 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+4)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+16& = &15-14-x \\\Leftrightarrow & 12x \color{red}{+16} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &1-16 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-4)& = & 8 \color{red}{-} (-13+x) \\\Leftrightarrow & -30x-24& = &8+13-x \\\Leftrightarrow & -30x \color{red}{-24} & = &21 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &21+24 \\\Leftrightarrow & -29x& = &45 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{45}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-45}{29} & & \\ & V = \left\{ \frac{-45}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x+6)& = & -7 \color{red}{-} (-2+x) \\\Leftrightarrow & -9x+18& = &-7+2-x \\\Leftrightarrow & -9x \color{red}{+18} & = &-5 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -9x+x& = &-5-18 \\\Leftrightarrow & -8x& = &-23 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-23}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{23}{8} & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x-2)& = & -12 \color{red}{-} (5+x) \\\Leftrightarrow & -2x-4& = &-12-5-x \\\Leftrightarrow & -2x \color{red}{-4} & = &-17 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -2x+x& = &-17+4 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-3)& = & 4 \color{red}{+} (9+x) \\\Leftrightarrow & -6x-6& = &4+9+x \\\Leftrightarrow & -6x \color{red}{-6} & = &13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &13+6 \\\Leftrightarrow & -7x& = &19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+5)& = & 1 \color{red}{+} (-8+3x) \\\Leftrightarrow & -10x+10& = &1-8+3x \\\Leftrightarrow & -10x \color{red}{+10} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -10x-3x& = &-7-10 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+5)& = & -4 \color{red}{-} (-4-5x) \\\Leftrightarrow & -6x+30& = &-4+4+5x \\\Leftrightarrow & -6x \color{red}{+30} & = &0 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & -6x-5x& = &0-30 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x+6)& = & 10 \color{red}{+} (5+3x) \\\Leftrightarrow & 5x+30& = &10+5+3x \\\Leftrightarrow & 5x \color{red}{+30} & = &15 \color{red}{+3x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 5x-3x& = &15-30 \\\Leftrightarrow & 2x& = &-15 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-15}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-15}{2} & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)