Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x-1)& = & 8 \color{red}{-} (11-2x) \\\Leftrightarrow & 15x-3& = &8-11+2x \\\Leftrightarrow & 15x \color{red}{-3} & = &-3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 15x-2x& = &-3+3 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x-7)& = & -8 \color{red}{-} (-1+x) \\\Leftrightarrow & 4x-28& = &-8+1-x \\\Leftrightarrow & 4x \color{red}{-28} & = &-7 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 4x+x& = &-7+28 \\\Leftrightarrow & 5x& = &21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-2)& = & -9 \color{red}{+} (-13+3x) \\\Leftrightarrow & 4x-4& = &-9-13+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &-22+4 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x+2)& = & -7 \color{red}{-} (-9-2x) \\\Leftrightarrow & 15x+10& = &-7+9+2x \\\Leftrightarrow & 15x \color{red}{+10} & = &2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 15x-2x& = &2-10 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-6)& = & 3 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-12& = &3+5-x \\\Leftrightarrow & 12x \color{red}{-12} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &8+12 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+5)& = & 5 \color{red}{-} (5+x) \\\Leftrightarrow & 24x+20& = &5-5-x \\\Leftrightarrow & 24x \color{red}{+20} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 24x+x& = &0-20 \\\Leftrightarrow & 25x& = &-20 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-20}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-7)& = & 10 \color{red}{-} (12-2x) \\\Leftrightarrow & 9x-21& = &10-12+2x \\\Leftrightarrow & 9x \color{red}{-21} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 9x-2x& = &-2+21 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x-5)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & 8x-20& = &-9+5-x \\\Leftrightarrow & 8x \color{red}{-20} & = &-4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 8x+x& = &-4+20 \\\Leftrightarrow & 9x& = &16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-7)& = & -13 \color{red}{+} (6-4x) \\\Leftrightarrow & -9x-21& = &-13+6-4x \\\Leftrightarrow & -9x \color{red}{-21} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -9x+4x& = &-7+21 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x+4)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+12& = &-5-5+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-10-12 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-7)& = & 15 \color{red}{-} (11-5x) \\\Leftrightarrow & -16x-28& = &15-11+5x \\\Leftrightarrow & -16x \color{red}{-28} & = &4 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -16x-5x& = &4+28 \\\Leftrightarrow & -21x& = &32 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{32}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-32}{21} & & \\ & V = \left\{ \frac{-32}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+2)& = & 2 \color{red}{+} (5+x) \\\Leftrightarrow & 6x+6& = &2+5+x \\\Leftrightarrow & 6x \color{red}{+6} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &7-6 \\\Leftrightarrow & 5x& = &1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)