Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x-3)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-9& = &-7-12+x \\\Leftrightarrow & 12x \color{red}{-9} & = &-19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &-19+9 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+5)& = & -14 \color{red}{-} (-1+3x) \\\Leftrightarrow & -4x+20& = &-14+1-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &-13-20 \\\Leftrightarrow & -x& = &-33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-33}{ \color{red}{-1} } \\\Leftrightarrow & x = 33 & & \\ & V = \left\{ 33 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-4)& = & -2 \color{red}{+} (-4-3x) \\\Leftrightarrow & -10x-8& = &-2-4-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &-6 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &-6+8 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+1)& = & 7 \color{red}{-} (-13+3x) \\\Leftrightarrow & -20x+4& = &7+13-3x \\\Leftrightarrow & -20x \color{red}{+4} & = &20 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -20x+3x& = &20-4 \\\Leftrightarrow & -17x& = &16 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{16}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-16}{17} & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+2)& = & -2 \color{red}{-} (2+x) \\\Leftrightarrow & -3x+6& = &-2-2-x \\\Leftrightarrow & -3x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -3x+x& = &-4-6 \\\Leftrightarrow & -2x& = &-10 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-10}{ \color{red}{-2} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-1)& = & -4 \color{red}{-} (5+x) \\\Leftrightarrow & 24x-4& = &-4-5-x \\\Leftrightarrow & 24x \color{red}{-4} & = &-9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &-9+4 \\\Leftrightarrow & 25x& = &-5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x+5)& = & 8 \color{red}{-} (10-4x) \\\Leftrightarrow & -9x+15& = &8-10+4x \\\Leftrightarrow & -9x \color{red}{+15} & = &-2 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -9x-4x& = &-2-15 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-2)& = & -1 \color{red}{-} (-5-2x) \\\Leftrightarrow & -15x-6& = &-1+5+2x \\\Leftrightarrow & -15x \color{red}{-6} & = &4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -15x-2x& = &4+6 \\\Leftrightarrow & -17x& = &10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+2)& = & -11 \color{red}{+} (15+x) \\\Leftrightarrow & -6x+4& = &-11+15+x \\\Leftrightarrow & -6x \color{red}{+4} & = &4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -6x-x& = &4-4 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+3)& = & 14 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+6& = &14+6+x \\\Leftrightarrow & -12x \color{red}{+6} & = &20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &20-6 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-5)& = & -7 \color{red}{+} (8-5x) \\\Leftrightarrow & 6x-30& = &-7+8-5x \\\Leftrightarrow & 6x \color{red}{-30} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 6x+5x& = &1+30 \\\Leftrightarrow & 11x& = &31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{31}{11} & & \\ & V = \left\{ \frac{31}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+1)& = & -15 \color{red}{+} (15-2x) \\\Leftrightarrow & -15x+5& = &-15+15-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &0 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &0-5 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)