Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+6)& = & 11 \color{red}{-} (-7+x) \\\Leftrightarrow & -6x+12& = &11+7-x \\\Leftrightarrow & -6x \color{red}{+12} & = &18 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &18-12 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+6)& = & 10 \color{red}{-} (5-5x) \\\Leftrightarrow & 18x+36& = &10-5+5x \\\Leftrightarrow & 18x \color{red}{+36} & = &5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 18x-5x& = &5-36 \\\Leftrightarrow & 13x& = &-31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x+3)& = & -7 \color{red}{-} (4-5x) \\\Leftrightarrow & 36x+18& = &-7-4+5x \\\Leftrightarrow & 36x \color{red}{+18} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 36x-5x& = &-11-18 \\\Leftrightarrow & 31x& = &-29 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-29}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+2)& = & -1 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x+10& = &-1-8-2x \\\Leftrightarrow & -15x \color{red}{+10} & = &-9 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -15x+2x& = &-9-10 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-2)& = & -14 \color{red}{+} (9+x) \\\Leftrightarrow & -4x-8& = &-14+9+x \\\Leftrightarrow & -4x \color{red}{-8} & = &-5 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &-5+8 \\\Leftrightarrow & -5x& = &3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-1)& = & 15 \color{red}{+} (-9-2x) \\\Leftrightarrow & 5x-5& = &15-9-2x \\\Leftrightarrow & 5x \color{red}{-5} & = &6 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 5x+2x& = &6+5 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-7)& = & 12 \color{red}{-} (-2-2x) \\\Leftrightarrow & -15x-35& = &12+2+2x \\\Leftrightarrow & -15x \color{red}{-35} & = &14 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -15x-2x& = &14+35 \\\Leftrightarrow & -17x& = &49 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{49}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-49}{17} & & \\ & V = \left\{ \frac{-49}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+2)& = & 11 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x+6& = &11+14-x \\\Leftrightarrow & -6x \color{red}{+6} & = &25 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &25-6 \\\Leftrightarrow & -5x& = &19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-19}{5} & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+3)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & 20x+12& = &-11-7-x \\\Leftrightarrow & 20x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 20x+x& = &-18-12 \\\Leftrightarrow & 21x& = &-30 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-30}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+7)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & -2x+14& = &-13+6-x \\\Leftrightarrow & -2x \color{red}{+14} & = &-7 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -2x+x& = &-7-14 \\\Leftrightarrow & -x& = &-21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-21}{ \color{red}{-1} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x-6)& = & -8 \color{red}{+} (15+2x) \\\Leftrightarrow & -25x-30& = &-8+15+2x \\\Leftrightarrow & -25x \color{red}{-30} & = &7 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & -25x-2x& = &7+30 \\\Leftrightarrow & -27x& = &37 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{37}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-37}{27} & & \\ & V = \left\{ \frac{-37}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+6)& = & 4 \color{red}{-} (10-5x) \\\Leftrightarrow & 6x+12& = &4-10+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &-6-12 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)