Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x+3)& = & 1 \color{red}{+} (-1+2x) \\\Leftrightarrow & 5x+15& = &1-1+2x \\\Leftrightarrow & 5x \color{red}{+15} & = &0 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 5x-2x& = &0-15 \\\Leftrightarrow & 3x& = &-15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-15}{ \color{red}{3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-1)& = & -7 \color{red}{-} (-5-5x) \\\Leftrightarrow & 18x-3& = &-7+5+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &-2+3 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+1)& = & -8 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x+3& = &-8+2-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-6-3 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+4)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & 36x+24& = &-6-7-x \\\Leftrightarrow & 36x \color{red}{+24} & = &-13 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 36x+x& = &-13-24 \\\Leftrightarrow & 37x& = &-37 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-37}{ \color{red}{37} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-2)& = & 3 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x-8& = &3+6+5x \\\Leftrightarrow & -8x \color{red}{-8} & = &9 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -8x-5x& = &9+8 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+3)& = & -15 \color{red}{+} (7+x) \\\Leftrightarrow & 12x+18& = &-15+7+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-8-18 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x+5)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & -6x+30& = &-2-9+x \\\Leftrightarrow & -6x \color{red}{+30} & = &-11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -6x-x& = &-11-30 \\\Leftrightarrow & -7x& = &-41 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-41}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{41}{7} & & \\ & V = \left\{ \frac{41}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+2)& = & 9 \color{red}{+} (-13-5x) \\\Leftrightarrow & -16x+8& = &9-13-5x \\\Leftrightarrow & -16x \color{red}{+8} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -16x+5x& = &-4-8 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+1)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+6& = &-8-12+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-20-6 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x-3)& = & -9 \color{red}{-} (-1+x) \\\Leftrightarrow & -6x-9& = &-9+1-x \\\Leftrightarrow & -6x \color{red}{-9} & = &-8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -6x+x& = &-8+9 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-4)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & -8x-8& = &12-13-x \\\Leftrightarrow & -8x \color{red}{-8} & = &-1 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &-1+8 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+6)& = & -7 \color{red}{+} (12+2x) \\\Leftrightarrow & 15x+18& = &-7+12+2x \\\Leftrightarrow & 15x \color{red}{+18} & = &5 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 15x-2x& = &5-18 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)