Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+5)& = & -1 \color{red}{-} (11-3x) \\\Leftrightarrow & 16x+20& = &-1-11+3x \\\Leftrightarrow & 16x \color{red}{+20} & = &-12 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 16x-3x& = &-12-20 \\\Leftrightarrow & 13x& = &-32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+5)& = & 1 \color{red}{+} (1+x) \\\Leftrightarrow & -5x+25& = &1+1+x \\\Leftrightarrow & -5x \color{red}{+25} & = &2 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -5x-x& = &2-25 \\\Leftrightarrow & -6x& = &-23 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-23}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{23}{6} & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x+7)& = & -1 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+14& = &-1+12-x \\\Leftrightarrow & -12x \color{red}{+14} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &11-14 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x+7)& = & 7 \color{red}{+} (-9-5x) \\\Leftrightarrow & -18x+21& = &7-9-5x \\\Leftrightarrow & -18x \color{red}{+21} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -18x+5x& = &-2-21 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+1)& = & 13 \color{red}{+} (-8-5x) \\\Leftrightarrow & 6x+3& = &13-8-5x \\\Leftrightarrow & 6x \color{red}{+3} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 6x+5x& = &5-3 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+7)& = & -14 \color{red}{-} (-3+3x) \\\Leftrightarrow & -8x+14& = &-14+3-3x \\\Leftrightarrow & -8x \color{red}{+14} & = &-11 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -8x+3x& = &-11-14 \\\Leftrightarrow & -5x& = &-25 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-25}{ \color{red}{-5} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+1)& = & 2 \color{red}{+} (-8+x) \\\Leftrightarrow & -36x+6& = &2-8+x \\\Leftrightarrow & -36x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -36x-x& = &-6-6 \\\Leftrightarrow & -37x& = &-12 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-12}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{12}{37} & & \\ & V = \left\{ \frac{12}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+2)& = & 8 \color{red}{+} (3+x) \\\Leftrightarrow & -18x+6& = &8+3+x \\\Leftrightarrow & -18x \color{red}{+6} & = &11 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &11-6 \\\Leftrightarrow & -19x& = &5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+5)& = & -7 \color{red}{+} (-6+x) \\\Leftrightarrow & -6x+10& = &-7-6+x \\\Leftrightarrow & -6x \color{red}{+10} & = &-13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -6x-x& = &-13-10 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-1)& = & -5 \color{red}{-} (-2+x) \\\Leftrightarrow & -6x-6& = &-5+2-x \\\Leftrightarrow & -6x \color{red}{-6} & = &-3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &-3+6 \\\Leftrightarrow & -5x& = &3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x-3)& = & 13 \color{red}{-} (14+x) \\\Leftrightarrow & 12x-18& = &13-14-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-1+18 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+6)& = & -2 \color{red}{+} (13+x) \\\Leftrightarrow & 30x+30& = &-2+13+x \\\Leftrightarrow & 30x \color{red}{+30} & = &11 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &11-30 \\\Leftrightarrow & 29x& = &-19 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-19}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)