Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+7)& = & 11 \color{red}{-} (5+x) \\\Leftrightarrow & 4x+14& = &11-5-x \\\Leftrightarrow & 4x \color{red}{+14} & = &6 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 4x+x& = &6-14 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+6)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & 30x+36& = &11+5-x \\\Leftrightarrow & 30x \color{red}{+36} & = &16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &16-36 \\\Leftrightarrow & 31x& = &-20 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-20}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-20}{31} & & \\ & V = \left\{ \frac{-20}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+7)& = & -8 \color{red}{-} (-6+x) \\\Leftrightarrow & 20x+28& = &-8+6-x \\\Leftrightarrow & 20x \color{red}{+28} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &-2-28 \\\Leftrightarrow & 21x& = &-30 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-30}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+4)& = & -8 \color{red}{-} (-8+x) \\\Leftrightarrow & -12x+8& = &-8+8-x \\\Leftrightarrow & -12x \color{red}{+8} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &0-8 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+4)& = & -5 \color{red}{-} (12+x) \\\Leftrightarrow & 24x+24& = &-5-12-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-17-24 \\\Leftrightarrow & 25x& = &-41 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-41}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-41}{25} & & \\ & V = \left\{ \frac{-41}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x+1)& = & -13 \color{red}{+} (-5-5x) \\\Leftrightarrow & -6x+3& = &-13-5-5x \\\Leftrightarrow & -6x \color{red}{+3} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & -6x+5x& = &-18-3 \\\Leftrightarrow & -x& = &-21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-21}{ \color{red}{-1} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-2)& = & -2 \color{red}{+} (6+x) \\\Leftrightarrow & -36x-12& = &-2+6+x \\\Leftrightarrow & -36x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -36x-x& = &4+12 \\\Leftrightarrow & -37x& = &16 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{16}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-16}{37} & & \\ & V = \left\{ \frac{-16}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+6)& = & -9 \color{red}{+} (12-5x) \\\Leftrightarrow & 18x+18& = &-9+12-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &3 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &3-18 \\\Leftrightarrow & 23x& = &-15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-1)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -3x-3& = &-7-8+x \\\Leftrightarrow & -3x \color{red}{-3} & = &-15 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -3x-x& = &-15+3 \\\Leftrightarrow & -4x& = &-12 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-12}{ \color{red}{-4} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x-1)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & -30x-5& = &3-6-x \\\Leftrightarrow & -30x \color{red}{-5} & = &-3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &-3+5 \\\Leftrightarrow & -29x& = &2 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{2}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+7)& = & 14 \color{red}{+} (14-5x) \\\Leftrightarrow & -18x+42& = &14+14-5x \\\Leftrightarrow & -18x \color{red}{+42} & = &28 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &28 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -18x+5x& = &28-42 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+6)& = & 7 \color{red}{-} (8+x) \\\Leftrightarrow & -18x+36& = &7-8-x \\\Leftrightarrow & -18x \color{red}{+36} & = &-1 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -18x+x& = &-1-36 \\\Leftrightarrow & -17x& = &-37 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-37}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{37}{17} & & \\ & V = \left\{ \frac{37}{17} \right\} & \\\end{align}\)