Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-2)& = & 3 \color{red}{+} (-5+x) \\\Leftrightarrow & -2x-4& = &3-5+x \\\Leftrightarrow & -2x \color{red}{-4} & = &-2 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &-2+4 \\\Leftrightarrow & -3x& = &2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-1)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & -15x-5& = &-1+5-x \\\Leftrightarrow & -15x \color{red}{-5} & = &4 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -15x+x& = &4+5 \\\Leftrightarrow & -14x& = &9 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{9}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-9}{14} & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+6)& = & -14 \color{red}{-} (-2-2x) \\\Leftrightarrow & -15x+18& = &-14+2+2x \\\Leftrightarrow & -15x \color{red}{+18} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -15x-2x& = &-12-18 \\\Leftrightarrow & -17x& = &-30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-2)& = & 1 \color{red}{+} (10+3x) \\\Leftrightarrow & 10x-4& = &1+10+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &11 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &11+4 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x+1)& = & -5 \color{red}{+} (-2+4x) \\\Leftrightarrow & -15x+3& = &-5-2+4x \\\Leftrightarrow & -15x \color{red}{+3} & = &-7 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & -15x-4x& = &-7-3 \\\Leftrightarrow & -19x& = &-10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+5)& = & -4 \color{red}{-} (-8-2x) \\\Leftrightarrow & -15x+25& = &-4+8+2x \\\Leftrightarrow & -15x \color{red}{+25} & = &4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & -15x-2x& = &4-25 \\\Leftrightarrow & -17x& = &-21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-6)& = & 11 \color{red}{-} (-6+4x) \\\Leftrightarrow & 9x-18& = &11+6-4x \\\Leftrightarrow & 9x \color{red}{-18} & = &17 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & 9x+4x& = &17+18 \\\Leftrightarrow & 13x& = &35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+5)& = & 3 \color{red}{-} (12+3x) \\\Leftrightarrow & -8x+10& = &3-12-3x \\\Leftrightarrow & -8x \color{red}{+10} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -8x+3x& = &-9-10 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-7)& = & -2 \color{red}{+} (1+4x) \\\Leftrightarrow & -15x-35& = &-2+1+4x \\\Leftrightarrow & -15x \color{red}{-35} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & -15x-4x& = &-1+35 \\\Leftrightarrow & -19x& = &34 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{34}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-34}{19} & & \\ & V = \left\{ \frac{-34}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+7)& = & -14 \color{red}{+} (-5-2x) \\\Leftrightarrow & 9x+21& = &-14-5-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &-19 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &-19-21 \\\Leftrightarrow & 11x& = &-40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-3)& = & 9 \color{red}{+} (-4-5x) \\\Leftrightarrow & -36x-18& = &9-4-5x \\\Leftrightarrow & -36x \color{red}{-18} & = &5 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -36x+5x& = &5+18 \\\Leftrightarrow & -31x& = &23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-23}{31} & & \\ & V = \left\{ \frac{-23}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+1)& = & 7 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x+4& = &7+7-3x \\\Leftrightarrow & 4x \color{red}{+4} & = &14 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 4x+3x& = &14-4 \\\Leftrightarrow & 7x& = &10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)