Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-3)& = & 1 \color{red}{+} (13+x) \\\Leftrightarrow & -30x-15& = &1+13+x \\\Leftrightarrow & -30x \color{red}{-15} & = &14 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &14+15 \\\Leftrightarrow & -31x& = &29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+5)& = & 8 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x+15& = &8-1+x \\\Leftrightarrow & 18x \color{red}{+15} & = &7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 18x-x& = &7-15 \\\Leftrightarrow & 17x& = &-8 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-8}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+7)& = & -2 \color{red}{-} (-7+2x) \\\Leftrightarrow & -9x+21& = &-2+7-2x \\\Leftrightarrow & -9x \color{red}{+21} & = &5 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -9x+2x& = &5-21 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-4)& = & -11 \color{red}{-} (5-2x) \\\Leftrightarrow & -25x-20& = &-11-5+2x \\\Leftrightarrow & -25x \color{red}{-20} & = &-16 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & -25x-2x& = &-16+20 \\\Leftrightarrow & -27x& = &4 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{4}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-4}{27} & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-3)& = & -14 \color{red}{-} (1+x) \\\Leftrightarrow & 15x-15& = &-14-1-x \\\Leftrightarrow & 15x \color{red}{-15} & = &-15 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 15x+x& = &-15+15 \\\Leftrightarrow & 16x& = &0 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{0}{ \color{red}{16} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+7)& = & -12 \color{red}{-} (12-3x) \\\Leftrightarrow & 10x+35& = &-12-12+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-24 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &-24-35 \\\Leftrightarrow & 7x& = &-59 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-59}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-59}{7} & & \\ & V = \left\{ \frac{-59}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-7)& = & 12 \color{red}{-} (1-5x) \\\Leftrightarrow & -18x-21& = &12-1+5x \\\Leftrightarrow & -18x \color{red}{-21} & = &11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -18x-5x& = &11+21 \\\Leftrightarrow & -23x& = &32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-32}{23} & & \\ & V = \left\{ \frac{-32}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+6)& = & -9 \color{red}{+} (6-3x) \\\Leftrightarrow & -10x+12& = &-9+6-3x \\\Leftrightarrow & -10x \color{red}{+12} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -10x+3x& = &-3-12 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-3)& = & -7 \color{red}{-} (-11+3x) \\\Leftrightarrow & 20x-15& = &-7+11-3x \\\Leftrightarrow & 20x \color{red}{-15} & = &4 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 20x+3x& = &4+15 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-2)& = & 12 \color{red}{-} (14+x) \\\Leftrightarrow & 15x-6& = &12-14-x \\\Leftrightarrow & 15x \color{red}{-6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 15x+x& = &-2+6 \\\Leftrightarrow & 16x& = &4 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{4}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+3)& = & 3 \color{red}{+} (-13+x) \\\Leftrightarrow & 30x+18& = &3-13+x \\\Leftrightarrow & 30x \color{red}{+18} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 30x-x& = &-10-18 \\\Leftrightarrow & 29x& = &-28 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-28}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-4)& = & -5 \color{red}{-} (7+x) \\\Leftrightarrow & 8x-8& = &-5-7-x \\\Leftrightarrow & 8x \color{red}{-8} & = &-12 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &-12+8 \\\Leftrightarrow & 9x& = &-4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)