Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+3)& = & 8 \color{red}{+} (14-3x) \\\Leftrightarrow & -4x+6& = &8+14-3x \\\Leftrightarrow & -4x \color{red}{+6} & = &22 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & -4x+3x& = &22-6 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-3)& = & -15 \color{red}{-} (10+x) \\\Leftrightarrow & -4x-6& = &-15-10-x \\\Leftrightarrow & -4x \color{red}{-6} & = &-25 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &-25+6 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+3)& = & -14 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x+9& = &-14-1-5x \\\Leftrightarrow & -18x \color{red}{+9} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -18x+5x& = &-15-9 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+3)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & -30x+15& = &7-9-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-2-15 \\\Leftrightarrow & -29x& = &-17 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-17}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{17}{29} & & \\ & V = \left\{ \frac{17}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+7)& = & 9 \color{red}{+} (3-5x) \\\Leftrightarrow & -18x+21& = &9+3-5x \\\Leftrightarrow & -18x \color{red}{+21} & = &12 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -18x+5x& = &12-21 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-2)& = & 8 \color{red}{+} (-6+4x) \\\Leftrightarrow & -5x-10& = &8-6+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &2 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &2+10 \\\Leftrightarrow & -9x& = &12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-6)& = & -8 \color{red}{-} (-13+4x) \\\Leftrightarrow & -9x-18& = &-8+13-4x \\\Leftrightarrow & -9x \color{red}{-18} & = &5 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & -9x+4x& = &5+18 \\\Leftrightarrow & -5x& = &23 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{23}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+2)& = & 5 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x+4& = &5+3-x \\\Leftrightarrow & 12x \color{red}{+4} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &8-4 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x-6)& = & 11 \color{red}{+} (-10+x) \\\Leftrightarrow & 30x-30& = &11-10+x \\\Leftrightarrow & 30x \color{red}{-30} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &1+30 \\\Leftrightarrow & 29x& = &31 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{31}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{31}{29} & & \\ & V = \left\{ \frac{31}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-1)& = & 4 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-4& = &4+6-x \\\Leftrightarrow & -24x \color{red}{-4} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &10+4 \\\Leftrightarrow & -23x& = &14 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{14}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-14}{23} & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-2)& = & 8 \color{red}{+} (1+x) \\\Leftrightarrow & -4x-4& = &8+1+x \\\Leftrightarrow & -4x \color{red}{-4} & = &9 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -4x-x& = &9+4 \\\Leftrightarrow & -5x& = &13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+1)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & -18x+6& = &-7+7-x \\\Leftrightarrow & -18x \color{red}{+6} & = &0 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -18x+x& = &0-6 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)