Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x-1)& = & 4 \color{red}{-} (14-3x) \\\Leftrightarrow & 10x-5& = &4-14+3x \\\Leftrightarrow & 10x \color{red}{-5} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & 10x-3x& = &-10+5 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x-3)& = & 12 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-6& = &12+1-x \\\Leftrightarrow & -12x \color{red}{-6} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &13+6 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-6)& = & -6 \color{red}{+} (8+x) \\\Leftrightarrow & -9x-18& = &-6+8+x \\\Leftrightarrow & -9x \color{red}{-18} & = &2 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -9x-x& = &2+18 \\\Leftrightarrow & -10x& = &20 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{20}{ \color{red}{-10} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-3)& = & -11 \color{red}{+} (11+x) \\\Leftrightarrow & 15x-15& = &-11+11+x \\\Leftrightarrow & 15x \color{red}{-15} & = &0 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 15x-x& = &0+15 \\\Leftrightarrow & 14x& = &15 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{15}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{15}{14} & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+5)& = & 10 \color{red}{-} (11+2x) \\\Leftrightarrow & 25x+25& = &10-11-2x \\\Leftrightarrow & 25x \color{red}{+25} & = &-1 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 25x+2x& = &-1-25 \\\Leftrightarrow & 27x& = &-26 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{-26}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{-26}{27} & & \\ & V = \left\{ \frac{-26}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-3)& = & -5 \color{red}{-} (15+x) \\\Leftrightarrow & -12x-9& = &-5-15-x \\\Leftrightarrow & -12x \color{red}{-9} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &-20+9 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-1)& = & -13 \color{red}{-} (9-3x) \\\Leftrightarrow & 10x-2& = &-13-9+3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & 10x-3x& = &-22+2 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x+1)& = & 15 \color{red}{-} (-13-2x) \\\Leftrightarrow & 15x+3& = &15+13+2x \\\Leftrightarrow & 15x \color{red}{+3} & = &28 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &28 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 15x-2x& = &28-3 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-5)& = & -14 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-10& = &-14+5-x \\\Leftrightarrow & 12x \color{red}{-10} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 12x+x& = &-9+10 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+7)& = & 9 \color{red}{+} (10+x) \\\Leftrightarrow & -16x+28& = &9+10+x \\\Leftrightarrow & -16x \color{red}{+28} & = &19 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -16x-x& = &19-28 \\\Leftrightarrow & -17x& = &-9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+7)& = & -10 \color{red}{+} (6+x) \\\Leftrightarrow & -8x+14& = &-10+6+x \\\Leftrightarrow & -8x \color{red}{+14} & = &-4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -8x-x& = &-4-14 \\\Leftrightarrow & -9x& = &-18 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-18}{ \color{red}{-9} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-5)& = & 5 \color{red}{-} (-3-5x) \\\Leftrightarrow & -6x-30& = &5+3+5x \\\Leftrightarrow & -6x \color{red}{-30} & = &8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -6x-5x& = &8+30 \\\Leftrightarrow & -11x& = &38 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{38}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)