Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x+3)& = & -10 \color{red}{+} (5+x) \\\Leftrightarrow & -10x+6& = &-10+5+x \\\Leftrightarrow & -10x \color{red}{+6} & = &-5 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -10x-x& = &-5-6 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+7)& = & -13 \color{red}{-} (-6-5x) \\\Leftrightarrow & 6x+21& = &-13+6+5x \\\Leftrightarrow & 6x \color{red}{+21} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 6x-5x& = &-7-21 \\\Leftrightarrow & x& = &-28 \\ & V = \left\{ -28 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-3)& = & -1 \color{red}{+} (1+x) \\\Leftrightarrow & -20x-15& = &-1+1+x \\\Leftrightarrow & -20x \color{red}{-15} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &0+15 \\\Leftrightarrow & -21x& = &15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+5)& = & -13 \color{red}{-} (9+x) \\\Leftrightarrow & 2x+10& = &-13-9-x \\\Leftrightarrow & 2x \color{red}{+10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 2x+x& = &-22-10 \\\Leftrightarrow & 3x& = &-32 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-32}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-32}{3} & & \\ & V = \left\{ \frac{-32}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-4)& = & -5 \color{red}{+} (-3-2x) \\\Leftrightarrow & -3x-12& = &-5-3-2x \\\Leftrightarrow & -3x \color{red}{-12} & = &-8 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -3x+2x& = &-8+12 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-7)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & 15x-21& = &-1-8-x \\\Leftrightarrow & 15x \color{red}{-21} & = &-9 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 15x+x& = &-9+21 \\\Leftrightarrow & 16x& = &12 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{12}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x-1)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & 8x-2& = &7-11+x \\\Leftrightarrow & 8x \color{red}{-2} & = &-4 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 8x-x& = &-4+2 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-1)& = & -6 \color{red}{+} (-1+x) \\\Leftrightarrow & -6x-6& = &-6-1+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-7+6 \\\Leftrightarrow & -7x& = &-1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-4)& = & -11 \color{red}{-} (-15+2x) \\\Leftrightarrow & -5x-20& = &-11+15-2x \\\Leftrightarrow & -5x \color{red}{-20} & = &4 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & -5x+2x& = &4+20 \\\Leftrightarrow & -3x& = &24 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{24}{ \color{red}{-3} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-7)& = & -8 \color{red}{-} (7+x) \\\Leftrightarrow & 24x-42& = &-8-7-x \\\Leftrightarrow & 24x \color{red}{-42} & = &-15 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &-15+42 \\\Leftrightarrow & 25x& = &27 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{27}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{27}{25} & & \\ & V = \left\{ \frac{27}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-3)& = & -10 \color{red}{-} (15+x) \\\Leftrightarrow & 12x-9& = &-10-15-x \\\Leftrightarrow & 12x \color{red}{-9} & = &-25 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &-25+9 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+7)& = & -10 \color{red}{+} (6+x) \\\Leftrightarrow & -4x+28& = &-10+6+x \\\Leftrightarrow & -4x \color{red}{+28} & = &-4 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -4x-x& = &-4-28 \\\Leftrightarrow & -5x& = &-32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)