Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x+1)& = & -8 \color{red}{-} (5-4x) \\\Leftrightarrow & 5x+5& = &-8-5+4x \\\Leftrightarrow & 5x \color{red}{+5} & = &-13 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 5x-4x& = &-13-5 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x+3)& = & 10 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+18& = &10+10-x \\\Leftrightarrow & -12x \color{red}{+18} & = &20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &20-18 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+3)& = & 15 \color{red}{+} (-2+3x) \\\Leftrightarrow & 8x+12& = &15-2+3x \\\Leftrightarrow & 8x \color{red}{+12} & = &13 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 8x-3x& = &13-12 \\\Leftrightarrow & 5x& = &1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-6)& = & -4 \color{red}{-} (15+x) \\\Leftrightarrow & 24x-24& = &-4-15-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-19 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-19+24 \\\Leftrightarrow & 25x& = &5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-3)& = & 15 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-15& = &15+14-x \\\Leftrightarrow & 30x \color{red}{-15} & = &29 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 30x+x& = &29+15 \\\Leftrightarrow & 31x& = &44 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{44}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{44}{31} & & \\ & V = \left\{ \frac{44}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x-4)& = & 5 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x-16& = &5+13-x \\\Leftrightarrow & -20x \color{red}{-16} & = &18 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &18+16 \\\Leftrightarrow & -19x& = &34 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{34}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-34}{19} & & \\ & V = \left\{ \frac{-34}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x-5)& = & 11 \color{red}{+} (15+x) \\\Leftrightarrow & 6x-15& = &11+15+x \\\Leftrightarrow & 6x \color{red}{-15} & = &26 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 6x-x& = &26+15 \\\Leftrightarrow & 5x& = &41 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{41}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{41}{5} & & \\ & V = \left\{ \frac{41}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x-5)& = & -9 \color{red}{+} (-7+x) \\\Leftrightarrow & 10x-25& = &-9-7+x \\\Leftrightarrow & 10x \color{red}{-25} & = &-16 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 10x-x& = &-16+25 \\\Leftrightarrow & 9x& = &9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{9}{ \color{red}{9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+6)& = & -2 \color{red}{+} (14+x) \\\Leftrightarrow & 2x+12& = &-2+14+x \\\Leftrightarrow & 2x \color{red}{+12} & = &12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 2x-x& = &12-12 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x+4)& = & -4 \color{red}{+} (13+x) \\\Leftrightarrow & -6x+24& = &-4+13+x \\\Leftrightarrow & -6x \color{red}{+24} & = &9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &9-24 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-6)& = & 6 \color{red}{+} (6-5x) \\\Leftrightarrow & -6x-12& = &6+6-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &12 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &12+12 \\\Leftrightarrow & -x& = &24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{24}{ \color{red}{-1} } \\\Leftrightarrow & x = -24 & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+7)& = & 5 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+28& = &5+13-x \\\Leftrightarrow & 12x \color{red}{+28} & = &18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &18-28 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)