Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+2)& = & 8 \color{red}{+} (-5+x) \\\Leftrightarrow & -9x+6& = &8-5+x \\\Leftrightarrow & -9x \color{red}{+6} & = &3 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -9x-x& = &3-6 \\\Leftrightarrow & -10x& = &-3 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-3}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-1)& = & -7 \color{red}{+} (-4+x) \\\Leftrightarrow & 25x-5& = &-7-4+x \\\Leftrightarrow & 25x \color{red}{-5} & = &-11 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 25x-x& = &-11+5 \\\Leftrightarrow & 24x& = &-6 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-6}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x-5)& = & 14 \color{red}{-} (-8+4x) \\\Leftrightarrow & -15x-15& = &14+8-4x \\\Leftrightarrow & -15x \color{red}{-15} & = &22 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -15x+4x& = &22+15 \\\Leftrightarrow & -11x& = &37 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{37}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-37}{11} & & \\ & V = \left\{ \frac{-37}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-4)& = & -3 \color{red}{-} (-9-4x) \\\Leftrightarrow & -25x-20& = &-3+9+4x \\\Leftrightarrow & -25x \color{red}{-20} & = &6 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -25x-4x& = &6+20 \\\Leftrightarrow & -29x& = &26 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{26}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-26}{29} & & \\ & V = \left\{ \frac{-26}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x-5)& = & -11 \color{red}{-} (-9+4x) \\\Leftrightarrow & -15x-25& = &-11+9-4x \\\Leftrightarrow & -15x \color{red}{-25} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -15x+4x& = &-2+25 \\\Leftrightarrow & -11x& = &23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+1)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+4& = &10+6-x \\\Leftrightarrow & 12x \color{red}{+4} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &16-4 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x+1)& = & -15 \color{red}{-} (4-5x) \\\Leftrightarrow & 8x+4& = &-15-4+5x \\\Leftrightarrow & 8x \color{red}{+4} & = &-19 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 8x-5x& = &-19-4 \\\Leftrightarrow & 3x& = &-23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-23}{3} & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+4)& = & -3 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x+8& = &-3+6-x \\\Leftrightarrow & -12x \color{red}{+8} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &3-8 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+5)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & -20x+25& = &-15+9+x \\\Leftrightarrow & -20x \color{red}{+25} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &-6-25 \\\Leftrightarrow & -21x& = &-31 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-31}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{31}{21} & & \\ & V = \left\{ \frac{31}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-2)& = & -11 \color{red}{+} (6+3x) \\\Leftrightarrow & -4x-8& = &-11+6+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-5+8 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+1)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & 10x+2& = &-10+14-x \\\Leftrightarrow & 10x \color{red}{+2} & = &4 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 10x+x& = &4-2 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-7)& = & 11 \color{red}{+} (6+x) \\\Leftrightarrow & 20x-28& = &11+6+x \\\Leftrightarrow & 20x \color{red}{-28} & = &17 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 20x-x& = &17+28 \\\Leftrightarrow & 19x& = &45 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{45}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{45}{19} & & \\ & V = \left\{ \frac{45}{19} \right\} & \\\end{align}\)