Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+2)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+4& = &-8-14+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-22 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-22-4 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+6)& = & -11 \color{red}{-} (-1+x) \\\Leftrightarrow & -20x+24& = &-11+1-x \\\Leftrightarrow & -20x \color{red}{+24} & = &-10 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -20x+x& = &-10-24 \\\Leftrightarrow & -19x& = &-34 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-34}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{34}{19} & & \\ & V = \left\{ \frac{34}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-3)& = & -8 \color{red}{+} (-15+x) \\\Leftrightarrow & -18x-18& = &-8-15+x \\\Leftrightarrow & -18x \color{red}{-18} & = &-23 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -18x-x& = &-23+18 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-7)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & 12x-42& = &8+11+x \\\Leftrightarrow & 12x \color{red}{-42} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &19+42 \\\Leftrightarrow & 11x& = &61 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{61}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{61}{11} & & \\ & V = \left\{ \frac{61}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-6)& = & 1 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-36& = &1-15-x \\\Leftrightarrow & 30x \color{red}{-36} & = &-14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &-14+36 \\\Leftrightarrow & 31x& = &22 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{22}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-7)& = & 10 \color{red}{+} (12+2x) \\\Leftrightarrow & 5x-35& = &10+12+2x \\\Leftrightarrow & 5x \color{red}{-35} & = &22 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 5x-2x& = &22+35 \\\Leftrightarrow & 3x& = &57 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{57}{ \color{red}{3} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x-3)& = & -10 \color{red}{+} (-10+x) \\\Leftrightarrow & 24x-18& = &-10-10+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-20 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-20+18 \\\Leftrightarrow & 23x& = &-2 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-2}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x-2)& = & 6 \color{red}{+} (15-2x) \\\Leftrightarrow & 15x-10& = &6+15-2x \\\Leftrightarrow & 15x \color{red}{-10} & = &21 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & 15x+2x& = &21+10 \\\Leftrightarrow & 17x& = &31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{31}{17} & & \\ & V = \left\{ \frac{31}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+6)& = & -7 \color{red}{-} (-3+2x) \\\Leftrightarrow & 9x+18& = &-7+3-2x \\\Leftrightarrow & 9x \color{red}{+18} & = &-4 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & 9x+2x& = &-4-18 \\\Leftrightarrow & 11x& = &-22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-22}{ \color{red}{11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+3)& = & 14 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x+15& = &14+14-x \\\Leftrightarrow & -30x \color{red}{+15} & = &28 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &28-15 \\\Leftrightarrow & -29x& = &13 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{13}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-4)& = & 6 \color{red}{-} (15+4x) \\\Leftrightarrow & -3x-12& = &6-15-4x \\\Leftrightarrow & -3x \color{red}{-12} & = &-9 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &-9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & -3x+4x& = &-9+12 \\\Leftrightarrow & x& = &3 \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+3)& = & -11 \color{red}{+} (-7+x) \\\Leftrightarrow & -2x+6& = &-11-7+x \\\Leftrightarrow & -2x \color{red}{+6} & = &-18 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -2x-x& = &-18-6 \\\Leftrightarrow & -3x& = &-24 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-24}{ \color{red}{-3} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)