Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-5)& = & -12 \color{red}{-} (3+x) \\\Leftrightarrow & 2x-10& = &-12-3-x \\\Leftrightarrow & 2x \color{red}{-10} & = &-15 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &-15+10 \\\Leftrightarrow & 3x& = &-5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x+4)& = & -14 \color{red}{+} (-11+x) \\\Leftrightarrow & -36x+24& = &-14-11+x \\\Leftrightarrow & -36x \color{red}{+24} & = &-25 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -36x-x& = &-25-24 \\\Leftrightarrow & -37x& = &-49 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-49}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{49}{37} & & \\ & V = \left\{ \frac{49}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-7)& = & -13 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-14& = &-13+15-x \\\Leftrightarrow & 12x \color{red}{-14} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &2+14 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x-5)& = & -2 \color{red}{-} (6+x) \\\Leftrightarrow & 18x-15& = &-2-6-x \\\Leftrightarrow & 18x \color{red}{-15} & = &-8 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 18x+x& = &-8+15 \\\Leftrightarrow & 19x& = &7 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{7}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+7)& = & -10 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+14& = &-10+6+x \\\Leftrightarrow & 12x \color{red}{+14} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 12x-x& = &-4-14 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x+2)& = & -11 \color{red}{+} (1+x) \\\Leftrightarrow & -6x+6& = &-11+1+x \\\Leftrightarrow & -6x \color{red}{+6} & = &-10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &-10-6 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x-6)& = & -9 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x-24& = &-9-3+x \\\Leftrightarrow & -20x \color{red}{-24} & = &-12 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &-12+24 \\\Leftrightarrow & -21x& = &12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x+2)& = & -15 \color{red}{-} (3+x) \\\Leftrightarrow & -4x+8& = &-15-3-x \\\Leftrightarrow & -4x \color{red}{+8} & = &-18 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -4x+x& = &-18-8 \\\Leftrightarrow & -3x& = &-26 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-26}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{26}{3} & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x-1)& = & -14 \color{red}{+} (6+x) \\\Leftrightarrow & 30x-6& = &-14+6+x \\\Leftrightarrow & 30x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &-8+6 \\\Leftrightarrow & 29x& = &-2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-2)& = & -1 \color{red}{-} (-10-5x) \\\Leftrightarrow & 6x-12& = &-1+10+5x \\\Leftrightarrow & 6x \color{red}{-12} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 6x-5x& = &9+12 \\\Leftrightarrow & x& = &21 \\ & V = \left\{ 21 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x-5)& = & -8 \color{red}{+} (11+4x) \\\Leftrightarrow & -25x-25& = &-8+11+4x \\\Leftrightarrow & -25x \color{red}{-25} & = &3 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & -25x-4x& = &3+25 \\\Leftrightarrow & -29x& = &28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x+6)& = & 4 \color{red}{-} (3+x) \\\Leftrightarrow & 12x+18& = &4-3-x \\\Leftrightarrow & 12x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &1-18 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)