Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+3)& = & 9 \color{red}{-} (-6-4x) \\\Leftrightarrow & 25x+15& = &9+6+4x \\\Leftrightarrow & 25x \color{red}{+15} & = &15 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 25x-4x& = &15-15 \\\Leftrightarrow & 21x& = &0 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{0}{ \color{red}{21} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x-1)& = & 2 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-2& = &2+5+x \\\Leftrightarrow & 12x \color{red}{-2} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &7+2 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-3)& = & 1 \color{red}{+} (-11-3x) \\\Leftrightarrow & -4x-12& = &1-11-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &-10 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &-10+12 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-3)& = & -9 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-6& = &-9-11+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-20+6 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-2)& = & -5 \color{red}{-} (-5+3x) \\\Leftrightarrow & -25x-10& = &-5+5-3x \\\Leftrightarrow & -25x \color{red}{-10} & = &0 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -25x+3x& = &0+10 \\\Leftrightarrow & -22x& = &10 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{10}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+2)& = & 7 \color{red}{+} (-10+x) \\\Leftrightarrow & 30x+12& = &7-10+x \\\Leftrightarrow & 30x \color{red}{+12} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 30x-x& = &-3-12 \\\Leftrightarrow & 29x& = &-15 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-15}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-15}{29} & & \\ & V = \left\{ \frac{-15}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-1)& = & 12 \color{red}{-} (-11+x) \\\Leftrightarrow & -30x-5& = &12+11-x \\\Leftrightarrow & -30x \color{red}{-5} & = &23 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &23+5 \\\Leftrightarrow & -29x& = &28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x+7)& = & 5 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x+35& = &5+9-x \\\Leftrightarrow & 30x \color{red}{+35} & = &14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &14-35 \\\Leftrightarrow & 31x& = &-21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-21}{31} & & \\ & V = \left\{ \frac{-21}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+1)& = & 10 \color{red}{-} (7+4x) \\\Leftrightarrow & 3x+3& = &10-7-4x \\\Leftrightarrow & 3x \color{red}{+3} & = &3 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 3x+4x& = &3-3 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-7)& = & 7 \color{red}{+} (15-2x) \\\Leftrightarrow & -15x-35& = &7+15-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &22 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &22 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &22+35 \\\Leftrightarrow & -13x& = &57 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{57}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-57}{13} & & \\ & V = \left\{ \frac{-57}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+2)& = & -5 \color{red}{+} (6+x) \\\Leftrightarrow & 36x+12& = &-5+6+x \\\Leftrightarrow & 36x \color{red}{+12} & = &1 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 36x-x& = &1-12 \\\Leftrightarrow & 35x& = &-11 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-11}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-11}{35} & & \\ & V = \left\{ \frac{-11}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+3)& = & 6 \color{red}{+} (-14+x) \\\Leftrightarrow & -30x+15& = &6-14+x \\\Leftrightarrow & -30x \color{red}{+15} & = &-8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -30x-x& = &-8-15 \\\Leftrightarrow & -31x& = &-23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{23}{31} & & \\ & V = \left\{ \frac{23}{31} \right\} & \\\end{align}\)