Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x+1)& = & 12 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+6& = &12-15+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-3-6 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-6)& = & -2 \color{red}{-} (11+x) \\\Leftrightarrow & 15x-18& = &-2-11-x \\\Leftrightarrow & 15x \color{red}{-18} & = &-13 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 15x+x& = &-13+18 \\\Leftrightarrow & 16x& = &5 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{5}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{5}{16} & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+7)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -20x+28& = &-6+15+x \\\Leftrightarrow & -20x \color{red}{+28} & = &9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -20x-x& = &9-28 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+6)& = & 11 \color{red}{+} (-4+4x) \\\Leftrightarrow & -9x+18& = &11-4+4x \\\Leftrightarrow & -9x \color{red}{+18} & = &7 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -9x-4x& = &7-18 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+3)& = & -7 \color{red}{-} (-3-3x) \\\Leftrightarrow & 4x+12& = &-7+3+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &-4-12 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-1)& = & -7 \color{red}{-} (-7+3x) \\\Leftrightarrow & 8x-4& = &-7+7-3x \\\Leftrightarrow & 8x \color{red}{-4} & = &0 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 8x+3x& = &0+4 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-3)& = & -12 \color{red}{-} (4-4x) \\\Leftrightarrow & 25x-15& = &-12-4+4x \\\Leftrightarrow & 25x \color{red}{-15} & = &-16 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &-16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 25x-4x& = &-16+15 \\\Leftrightarrow & 21x& = &-1 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-1}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x+3)& = & 9 \color{red}{+} (-3+x) \\\Leftrightarrow & 10x+15& = &9-3+x \\\Leftrightarrow & 10x \color{red}{+15} & = &6 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 10x-x& = &6-15 \\\Leftrightarrow & 9x& = &-9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-9}{ \color{red}{9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+4)& = & 12 \color{red}{-} (8-2x) \\\Leftrightarrow & 15x+12& = &12-8+2x \\\Leftrightarrow & 15x \color{red}{+12} & = &4 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & 15x-2x& = &4-12 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-4)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & -36x-24& = &-11-10+x \\\Leftrightarrow & -36x \color{red}{-24} & = &-21 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &-21+24 \\\Leftrightarrow & -37x& = &3 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{3}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-3}{37} & & \\ & V = \left\{ \frac{-3}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-6)& = & -6 \color{red}{+} (8+x) \\\Leftrightarrow & -5x-30& = &-6+8+x \\\Leftrightarrow & -5x \color{red}{-30} & = &2 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -5x-x& = &2+30 \\\Leftrightarrow & -6x& = &32 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{32}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-16}{3} & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+2)& = & -9 \color{red}{+} (11+x) \\\Leftrightarrow & -24x+8& = &-9+11+x \\\Leftrightarrow & -24x \color{red}{+8} & = &2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &2-8 \\\Leftrightarrow & -25x& = &-6 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-6}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)