Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-1)& = & -12 \color{red}{-} (-12-5x) \\\Leftrightarrow & -18x-3& = &-12+12+5x \\\Leftrightarrow & -18x \color{red}{-3} & = &0 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -18x-5x& = &0+3 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+6)& = & -14 \color{red}{+} (15+x) \\\Leftrightarrow & 24x+36& = &-14+15+x \\\Leftrightarrow & 24x \color{red}{+36} & = &1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 24x-x& = &1-36 \\\Leftrightarrow & 23x& = &-35 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-35}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-6)& = & 6 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x-18& = &6-4-2x \\\Leftrightarrow & 15x \color{red}{-18} & = &2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 15x+2x& = &2+18 \\\Leftrightarrow & 17x& = &20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-5)& = & -10 \color{red}{-} (-13-5x) \\\Leftrightarrow & -8x-10& = &-10+13+5x \\\Leftrightarrow & -8x \color{red}{-10} & = &3 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & -8x-5x& = &3+10 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-6)& = & -12 \color{red}{-} (5+3x) \\\Leftrightarrow & 4x-24& = &-12-5-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-17+24 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-1)& = & -3 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x-3& = &-3+4-5x \\\Leftrightarrow & -6x \color{red}{-3} & = &1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -6x+5x& = &1+3 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+6)& = & 4 \color{red}{+} (3-3x) \\\Leftrightarrow & -4x+12& = &4+3-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &7 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &7-12 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+1)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & 3x+3& = &-15+6+x \\\Leftrightarrow & 3x \color{red}{+3} & = &-9 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 3x-x& = &-9-3 \\\Leftrightarrow & 2x& = &-12 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-12}{ \color{red}{2} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x+7)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & -24x+28& = &12-13-x \\\Leftrightarrow & -24x \color{red}{+28} & = &-1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &-1-28 \\\Leftrightarrow & -23x& = &-29 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-29}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{29}{23} & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+1)& = & 15 \color{red}{-} (-1+x) \\\Leftrightarrow & -6x+3& = &15+1-x \\\Leftrightarrow & -6x \color{red}{+3} & = &16 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -6x+x& = &16-3 \\\Leftrightarrow & -5x& = &13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+1)& = & 10 \color{red}{+} (13+x) \\\Leftrightarrow & 24x+6& = &10+13+x \\\Leftrightarrow & 24x \color{red}{+6} & = &23 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 24x-x& = &23-6 \\\Leftrightarrow & 23x& = &17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+5)& = & -3 \color{red}{-} (9+x) \\\Leftrightarrow & 6x+15& = &-3-9-x \\\Leftrightarrow & 6x \color{red}{+15} & = &-12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &-12-15 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)