Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x+6)& = & 10 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x+30& = &10+4-x \\\Leftrightarrow & 30x \color{red}{+30} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &14-30 \\\Leftrightarrow & 31x& = &-16 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-16}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-16}{31} & & \\ & V = \left\{ \frac{-16}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x-4)& = & -8 \color{red}{+} (2+x) \\\Leftrightarrow & 12x-8& = &-8+2+x \\\Leftrightarrow & 12x \color{red}{-8} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &-6+8 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x+7)& = & 8 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+14& = &8+14-x \\\Leftrightarrow & -12x \color{red}{+14} & = &22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &22-14 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x+1)& = & 8 \color{red}{+} (5-2x) \\\Leftrightarrow & -3x+3& = &8+5-2x \\\Leftrightarrow & -3x \color{red}{+3} & = &13 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -3x+2x& = &13-3 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+5)& = & 3 \color{red}{+} (-9+x) \\\Leftrightarrow & -20x+20& = &3-9+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-6-20 \\\Leftrightarrow & -21x& = &-26 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-26}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x+1)& = & -7 \color{red}{-} (5-2x) \\\Leftrightarrow & 15x+3& = &-7-5+2x \\\Leftrightarrow & 15x \color{red}{+3} & = &-12 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 15x-2x& = &-12-3 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-3)& = & 5 \color{red}{-} (-8+x) \\\Leftrightarrow & 20x-15& = &5+8-x \\\Leftrightarrow & 20x \color{red}{-15} & = &13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 20x+x& = &13+15 \\\Leftrightarrow & 21x& = &28 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{28}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-2)& = & -3 \color{red}{-} (-7-3x) \\\Leftrightarrow & -10x-4& = &-3+7+3x \\\Leftrightarrow & -10x \color{red}{-4} & = &4 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -10x-3x& = &4+4 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+6)& = & -8 \color{red}{+} (-5+x) \\\Leftrightarrow & 30x+36& = &-8-5+x \\\Leftrightarrow & 30x \color{red}{+36} & = &-13 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &-13-36 \\\Leftrightarrow & 29x& = &-49 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-49}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-49}{29} & & \\ & V = \left\{ \frac{-49}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x+4)& = & -15 \color{red}{-} (-1+x) \\\Leftrightarrow & 25x+20& = &-15+1-x \\\Leftrightarrow & 25x \color{red}{+20} & = &-14 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 25x+x& = &-14-20 \\\Leftrightarrow & 26x& = &-34 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-34}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+7)& = & 12 \color{red}{+} (4+x) \\\Leftrightarrow & -24x+42& = &12+4+x \\\Leftrightarrow & -24x \color{red}{+42} & = &16 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &16-42 \\\Leftrightarrow & -25x& = &-26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x+1)& = & 6 \color{red}{+} (-2-5x) \\\Leftrightarrow & 36x+6& = &6-2-5x \\\Leftrightarrow & 36x \color{red}{+6} & = &4 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 36x+5x& = &4-6 \\\Leftrightarrow & 41x& = &-2 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-2}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-2}{41} & & \\ & V = \left\{ \frac{-2}{41} \right\} & \\\end{align}\)