Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x-4)& = & 14 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x-20& = &14+1-x \\\Leftrightarrow & 30x \color{red}{-20} & = &15 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &15+20 \\\Leftrightarrow & 31x& = &35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{35}{31} & & \\ & V = \left\{ \frac{35}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+4)& = & 15 \color{red}{-} (-13-5x) \\\Leftrightarrow & 8x+16& = &15+13+5x \\\Leftrightarrow & 8x \color{red}{+16} & = &28 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &28 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & 8x-5x& = &28-16 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-3)& = & 14 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-9& = &14+15-x \\\Leftrightarrow & -12x \color{red}{-9} & = &29 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &29+9 \\\Leftrightarrow & -11x& = &38 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{38}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+4)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+8& = &-8-14+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-22 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-22-8 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+7)& = & -2 \color{red}{+} (10-5x) \\\Leftrightarrow & -18x+21& = &-2+10-5x \\\Leftrightarrow & -18x \color{red}{+21} & = &8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -18x+5x& = &8-21 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x-6)& = & 4 \color{red}{+} (6+x) \\\Leftrightarrow & -6x-12& = &4+6+x \\\Leftrightarrow & -6x \color{red}{-12} & = &10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &10+12 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-4)& = & -9 \color{red}{+} (-9-2x) \\\Leftrightarrow & 15x-20& = &-9-9-2x \\\Leftrightarrow & 15x \color{red}{-20} & = &-18 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 15x+2x& = &-18+20 \\\Leftrightarrow & 17x& = &2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x+2)& = & -7 \color{red}{-} (2+x) \\\Leftrightarrow & 4x+8& = &-7-2-x \\\Leftrightarrow & 4x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 4x+x& = &-9-8 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+1)& = & 10 \color{red}{-} (-6-3x) \\\Leftrightarrow & 16x+4& = &10+6+3x \\\Leftrightarrow & 16x \color{red}{+4} & = &16 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 16x-3x& = &16-4 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-7)& = & 13 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x-14& = &13-13+x \\\Leftrightarrow & 6x \color{red}{-14} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 6x-x& = &0+14 \\\Leftrightarrow & 5x& = &14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-4)& = & 13 \color{red}{-} (5-4x) \\\Leftrightarrow & -5x-20& = &13-5+4x \\\Leftrightarrow & -5x \color{red}{-20} & = &8 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -5x-4x& = &8+20 \\\Leftrightarrow & -9x& = &28 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{28}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-28}{9} & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-3)& = & -11 \color{red}{+} (9+3x) \\\Leftrightarrow & 16x-12& = &-11+9+3x \\\Leftrightarrow & 16x \color{red}{-12} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 16x-3x& = &-2+12 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)