Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(-x-5)=11-(4+x)\)
2. \(4(4x+6)=-9+(8-5x)\)
3. \(2(-5x-1)=2+(-12-3x)\)
4. \(4(-5x-4)=9+(-3+x)\)
5. \(5(4x+2)=9-(2+x)\)
6. \(4(-3x-5)=-3+(15+x)\)
7. \(6(6x+1)=4-(13-5x)\)
8. \(3(-6x-1)=10-(3+x)\)
9. \(2(6x+4)=14+(-13+x)\)
10. \(2(3x-2)=-15+(3+x)\)
11. \(6(-x+7)=-9-(5+x)\)
12. \(4(-3x+2)=4-(7+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x-5)& = & 11 \color{red}{-} (4+x) \\\Leftrightarrow & -4x-20& = &11-4-x \\\Leftrightarrow & -4x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -4x+x& = &7+20 \\\Leftrightarrow & -3x& = &27 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{27}{ \color{red}{-3} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+6)& = & -9 \color{red}{+} (8-5x) \\\Leftrightarrow & 16x+24& = &-9+8-5x \\\Leftrightarrow & 16x \color{red}{+24} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 16x+5x& = &-1-24 \\\Leftrightarrow & 21x& = &-25 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-25}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-25}{21} & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-1)& = & 2 \color{red}{+} (-12-3x) \\\Leftrightarrow & -10x-2& = &2-12-3x \\\Leftrightarrow & -10x \color{red}{-2} & = &-10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -10x+3x& = &-10+2 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-4)& = & 9 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x-16& = &9-3+x \\\Leftrightarrow & -20x \color{red}{-16} & = &6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -20x-x& = &6+16 \\\Leftrightarrow & -21x& = &22 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{22}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x+2)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & 20x+10& = &9-2-x \\\Leftrightarrow & 20x \color{red}{+10} & = &7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 20x+x& = &7-10 \\\Leftrightarrow & 21x& = &-3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-5)& = & -3 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-20& = &-3+15+x \\\Leftrightarrow & -12x \color{red}{-20} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -12x-x& = &12+20 \\\Leftrightarrow & -13x& = &32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+1)& = & 4 \color{red}{-} (13-5x) \\\Leftrightarrow & 36x+6& = &4-13+5x \\\Leftrightarrow & 36x \color{red}{+6} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 36x-5x& = &-9-6 \\\Leftrightarrow & 31x& = &-15 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-15}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x-1)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & -18x-3& = &10-3-x \\\Leftrightarrow & -18x \color{red}{-3} & = &7 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -18x+x& = &7+3 \\\Leftrightarrow & -17x& = &10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x+4)& = & 14 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x+8& = &14-13+x \\\Leftrightarrow & 12x \color{red}{+8} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &1-8 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-2)& = & -15 \color{red}{+} (3+x) \\\Leftrightarrow & 6x-4& = &-15+3+x \\\Leftrightarrow & 6x \color{red}{-4} & = &-12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 6x-x& = &-12+4 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+7)& = & -9 \color{red}{-} (5+x) \\\Leftrightarrow & -6x+42& = &-9-5-x \\\Leftrightarrow & -6x \color{red}{+42} & = &-14 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -6x+x& = &-14-42 \\\Leftrightarrow & -5x& = &-56 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-56}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{56}{5} & & \\ & V = \left\{ \frac{56}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+2)& = & 4 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+8& = &4-7-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-3-8 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)