Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x+4)& = & 5 \color{red}{+} (3-2x) \\\Leftrightarrow & 5x+20& = &5+3-2x \\\Leftrightarrow & 5x \color{red}{+20} & = &8 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 5x+2x& = &8-20 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x-4)& = & 12 \color{red}{+} (-13-5x) \\\Leftrightarrow & 6x-24& = &12-13-5x \\\Leftrightarrow & 6x \color{red}{-24} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 6x+5x& = &-1+24 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-4)& = & -3 \color{red}{+} (8+x) \\\Leftrightarrow & 20x-20& = &-3+8+x \\\Leftrightarrow & 20x \color{red}{-20} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &5+20 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+3)& = & -14 \color{red}{-} (15+x) \\\Leftrightarrow & 18x+9& = &-14-15-x \\\Leftrightarrow & 18x \color{red}{+9} & = &-29 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-29 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 18x+x& = &-29-9 \\\Leftrightarrow & 19x& = &-38 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-38}{ \color{red}{19} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-1)& = & 3 \color{red}{-} (11+x) \\\Leftrightarrow & -18x-3& = &3-11-x \\\Leftrightarrow & -18x \color{red}{-3} & = &-8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -18x+x& = &-8+3 \\\Leftrightarrow & -17x& = &-5 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-5}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+5)& = & -1 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x+25& = &-1-6+x \\\Leftrightarrow & -30x \color{red}{+25} & = &-7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &-7-25 \\\Leftrightarrow & -31x& = &-32 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-32}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{32}{31} & & \\ & V = \left\{ \frac{32}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x+5)& = & 14 \color{red}{+} (-4-4x) \\\Leftrightarrow & -25x+25& = &14-4-4x \\\Leftrightarrow & -25x \color{red}{+25} & = &10 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & -25x+4x& = &10-25 \\\Leftrightarrow & -21x& = &-15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-1)& = & 1 \color{red}{+} (13+x) \\\Leftrightarrow & 2x-2& = &1+13+x \\\Leftrightarrow & 2x \color{red}{-2} & = &14 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 2x-x& = &14+2 \\\Leftrightarrow & x& = &16 \\ & V = \left\{ 16 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-5)& = & -3 \color{red}{-} (-1-3x) \\\Leftrightarrow & -4x-20& = &-3+1+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &-2+20 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-6)& = & -12 \color{red}{-} (15+3x) \\\Leftrightarrow & -8x-24& = &-12-15-3x \\\Leftrightarrow & -8x \color{red}{-24} & = &-27 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -8x+3x& = &-27+24 \\\Leftrightarrow & -5x& = &-3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+7)& = & -14 \color{red}{-} (-5+x) \\\Leftrightarrow & -3x+21& = &-14+5-x \\\Leftrightarrow & -3x \color{red}{+21} & = &-9 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -3x+x& = &-9-21 \\\Leftrightarrow & -2x& = &-30 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-30}{ \color{red}{-2} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (2x+2)& = & 5 \color{red}{-} (13+3x) \\\Leftrightarrow & 4x+4& = &5-13-3x \\\Leftrightarrow & 4x \color{red}{+4} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 4x+3x& = &-8-4 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)