Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-5)& = & -6 \color{red}{-} (-10+x) \\\Leftrightarrow & 8x-20& = &-6+10-x \\\Leftrightarrow & 8x \color{red}{-20} & = &4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 8x+x& = &4+20 \\\Leftrightarrow & 9x& = &24 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{24}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-5)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-15& = &11+3+x \\\Leftrightarrow & 12x \color{red}{-15} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &14+15 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x+1)& = & 5 \color{red}{+} (14+x) \\\Leftrightarrow & -3x+3& = &5+14+x \\\Leftrightarrow & -3x \color{red}{+3} & = &19 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -3x-x& = &19-3 \\\Leftrightarrow & -4x& = &16 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{16}{ \color{red}{-4} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-2)& = & 11 \color{red}{+} (4+4x) \\\Leftrightarrow & 25x-10& = &11+4+4x \\\Leftrightarrow & 25x \color{red}{-10} & = &15 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & 25x-4x& = &15+10 \\\Leftrightarrow & 21x& = &25 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{25}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{25}{21} & & \\ & V = \left\{ \frac{25}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-6)& = & 5 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x-30& = &5+9-x \\\Leftrightarrow & 30x \color{red}{-30} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &14+30 \\\Leftrightarrow & 31x& = &44 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{44}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{44}{31} & & \\ & V = \left\{ \frac{44}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-2)& = & -4 \color{red}{-} (-6+x) \\\Leftrightarrow & -9x-6& = &-4+6-x \\\Leftrightarrow & -9x \color{red}{-6} & = &2 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -9x+x& = &2+6 \\\Leftrightarrow & -8x& = &8 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{8}{ \color{red}{-8} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x+5)& = & 12 \color{red}{-} (10+4x) \\\Leftrightarrow & -9x+15& = &12-10-4x \\\Leftrightarrow & -9x \color{red}{+15} & = &2 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -9x+4x& = &2-15 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x-6)& = & -5 \color{red}{-} (13+x) \\\Leftrightarrow & 12x-36& = &-5-13-x \\\Leftrightarrow & 12x \color{red}{-36} & = &-18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 12x+x& = &-18+36 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+2)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x+8& = &-7-8+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-15-8 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-7)& = & -6 \color{red}{-} (-12-3x) \\\Leftrightarrow & -10x-14& = &-6+12+3x \\\Leftrightarrow & -10x \color{red}{-14} & = &6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -10x-3x& = &6+14 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+5)& = & -12 \color{red}{-} (-14-4x) \\\Leftrightarrow & 25x+25& = &-12+14+4x \\\Leftrightarrow & 25x \color{red}{+25} & = &2 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 25x-4x& = &2-25 \\\Leftrightarrow & 21x& = &-23 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-23}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-23}{21} & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-4)& = & 8 \color{red}{+} (5+x) \\\Leftrightarrow & 24x-16& = &8+5+x \\\Leftrightarrow & 24x \color{red}{-16} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 24x-x& = &13+16 \\\Leftrightarrow & 23x& = &29 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{29}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{29}{23} & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)