Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+1)& = & 4 \color{red}{-} (-4+x) \\\Leftrightarrow & -18x+3& = &4+4-x \\\Leftrightarrow & -18x \color{red}{+3} & = &8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -18x+x& = &8-3 \\\Leftrightarrow & -17x& = &5 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{5}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-7)& = & -10 \color{red}{-} (5+4x) \\\Leftrightarrow & 9x-21& = &-10-5-4x \\\Leftrightarrow & 9x \color{red}{-21} & = &-15 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &-15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 9x+4x& = &-15+21 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-4)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & -10x-8& = &14-14-x \\\Leftrightarrow & -10x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -10x+x& = &0+8 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+1)& = & 14 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+3& = &14+3+x \\\Leftrightarrow & -12x \color{red}{+3} & = &17 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &17-3 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+4)& = & 4 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+8& = &4-5-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-1-8 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-3)& = & -3 \color{red}{-} (9+x) \\\Leftrightarrow & 30x-15& = &-3-9-x \\\Leftrightarrow & 30x \color{red}{-15} & = &-12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 30x+x& = &-12+15 \\\Leftrightarrow & 31x& = &3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+4)& = & -2 \color{red}{+} (13+x) \\\Leftrightarrow & -8x+16& = &-2+13+x \\\Leftrightarrow & -8x \color{red}{+16} & = &11 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -8x-x& = &11-16 \\\Leftrightarrow & -9x& = &-5 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-5}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{5}{9} & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+4)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+24& = &11-10-x \\\Leftrightarrow & -24x \color{red}{+24} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &1-24 \\\Leftrightarrow & -23x& = &-23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-23}{ \color{red}{-23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-5)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & 24x-20& = &-3-13-x \\\Leftrightarrow & 24x \color{red}{-20} & = &-16 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &-16+20 \\\Leftrightarrow & 25x& = &4 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{4}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{4}{25} & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-3)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & -6x-6& = &15+7-x \\\Leftrightarrow & -6x \color{red}{-6} & = &22 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &22+6 \\\Leftrightarrow & -5x& = &28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-5)& = & -15 \color{red}{-} (1+x) \\\Leftrightarrow & 9x-15& = &-15-1-x \\\Leftrightarrow & 9x \color{red}{-15} & = &-16 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 9x+x& = &-16+15 \\\Leftrightarrow & 10x& = &-1 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-1}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-1)& = & 3 \color{red}{+} (-13+4x) \\\Leftrightarrow & 15x-3& = &3-13+4x \\\Leftrightarrow & 15x \color{red}{-3} & = &-10 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 15x-4x& = &-10+3 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)