Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x-6)& = & -7 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x-36& = &-7+11-x \\\Leftrightarrow & -24x \color{red}{-36} & = &4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &4+36 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x-1)& = & 13 \color{red}{-} (13+x) \\\Leftrightarrow & -30x-5& = &13-13-x \\\Leftrightarrow & -30x \color{red}{-5} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &0+5 \\\Leftrightarrow & -29x& = &5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-5}{29} & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+2)& = & 2 \color{red}{+} (6+x) \\\Leftrightarrow & -20x+8& = &2+6+x \\\Leftrightarrow & -20x \color{red}{+8} & = &8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &8-8 \\\Leftrightarrow & -21x& = &0 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{0}{ \color{red}{-21} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x+6)& = & 14 \color{red}{-} (13+x) \\\Leftrightarrow & 8x+24& = &14-13-x \\\Leftrightarrow & 8x \color{red}{+24} & = &1 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 8x+x& = &1-24 \\\Leftrightarrow & 9x& = &-23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-23}{9} & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x-3)& = & -1 \color{red}{+} (9+x) \\\Leftrightarrow & 10x-15& = &-1+9+x \\\Leftrightarrow & 10x \color{red}{-15} & = &8 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 10x-x& = &8+15 \\\Leftrightarrow & 9x& = &23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+4)& = & -4 \color{red}{-} (12+4x) \\\Leftrightarrow & 3x+12& = &-4-12-4x \\\Leftrightarrow & 3x \color{red}{+12} & = &-16 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & 3x+4x& = &-16-12 \\\Leftrightarrow & 7x& = &-28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-28}{ \color{red}{7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x-2)& = & -9 \color{red}{+} (11-5x) \\\Leftrightarrow & 6x-4& = &-9+11-5x \\\Leftrightarrow & 6x \color{red}{-4} & = &2 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 6x+5x& = &2+4 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+2)& = & 9 \color{red}{-} (-9-3x) \\\Leftrightarrow & -10x+10& = &9+9+3x \\\Leftrightarrow & -10x \color{red}{+10} & = &18 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -10x-3x& = &18-10 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-6)& = & -6 \color{red}{+} (1+x) \\\Leftrightarrow & -12x-36& = &-6+1+x \\\Leftrightarrow & -12x \color{red}{-36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -12x-x& = &-5+36 \\\Leftrightarrow & -13x& = &31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+2)& = & 9 \color{red}{-} (4-4x) \\\Leftrightarrow & -9x+6& = &9-4+4x \\\Leftrightarrow & -9x \color{red}{+6} & = &5 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & -9x-4x& = &5-6 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x+7)& = & 2 \color{red}{-} (13+x) \\\Leftrightarrow & 30x+35& = &2-13-x \\\Leftrightarrow & 30x \color{red}{+35} & = &-11 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &-11-35 \\\Leftrightarrow & 31x& = &-46 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-46}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-46}{31} & & \\ & V = \left\{ \frac{-46}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-4)& = & 9 \color{red}{-} (-1+x) \\\Leftrightarrow & -6x-24& = &9+1-x \\\Leftrightarrow & -6x \color{red}{-24} & = &10 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -6x+x& = &10+24 \\\Leftrightarrow & -5x& = &34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)