Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x+2)& = & -9 \color{red}{-} (2-3x) \\\Leftrightarrow & -4x+8& = &-9-2+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &-11-8 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-4)& = & -4 \color{red}{+} (9+x) \\\Leftrightarrow & -3x-12& = &-4+9+x \\\Leftrightarrow & -3x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -3x-x& = &5+12 \\\Leftrightarrow & -4x& = &17 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{17}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-17}{4} & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-2)& = & -8 \color{red}{-} (-2+x) \\\Leftrightarrow & 15x-6& = &-8+2-x \\\Leftrightarrow & 15x \color{red}{-6} & = &-6 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 15x+x& = &-6+6 \\\Leftrightarrow & 16x& = &0 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{0}{ \color{red}{16} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-3)& = & -4 \color{red}{+} (5+x) \\\Leftrightarrow & -6x-6& = &-4+5+x \\\Leftrightarrow & -6x \color{red}{-6} & = &1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &1+6 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-6)& = & -15 \color{red}{-} (12+3x) \\\Leftrightarrow & 4x-24& = &-15-12-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-27 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-27+24 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-6)& = & 3 \color{red}{+} (-7+x) \\\Leftrightarrow & -2x-12& = &3-7+x \\\Leftrightarrow & -2x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -2x-x& = &-4+12 \\\Leftrightarrow & -3x& = &8 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{8}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x+4)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x+16& = &6-7+x \\\Leftrightarrow & -12x \color{red}{+16} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -12x-x& = &-1-16 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+2)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+4& = &-9+10-x \\\Leftrightarrow & -12x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &1-4 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+5)& = & -4 \color{red}{-} (-12+3x) \\\Leftrightarrow & -8x+20& = &-4+12-3x \\\Leftrightarrow & -8x \color{red}{+20} & = &8 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -8x+3x& = &8-20 \\\Leftrightarrow & -5x& = &-12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-6)& = & 9 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-30& = &9-14+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-5+30 \\\Leftrightarrow & 29x& = &25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-2)& = & 8 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x-10& = &8+13-x \\\Leftrightarrow & -20x \color{red}{-10} & = &21 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &21+10 \\\Leftrightarrow & -19x& = &31 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{31}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-31}{19} & & \\ & V = \left\{ \frac{-31}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+5)& = & 10 \color{red}{+} (-15-5x) \\\Leftrightarrow & -18x+30& = &10-15-5x \\\Leftrightarrow & -18x \color{red}{+30} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -18x+5x& = &-5-30 \\\Leftrightarrow & -13x& = &-35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)